Math textbooks. Did you know that you can just buy math textbooks which are "several years too advanced for you"? And that due to economies of scale and the objectivity of their subject matter, they tend to be of both high and consistent quality? Not getting my parents to do this at that age is something I still regret decades later.

Or did you specifically mean fiction? If so, you're asking for fiction recommendations on the grew-up-reading-HPMOR website, we're obviously going to recommend HPMOR (especially if they've already read Harry Potter, but it's still good if you only know the broad strokes).

The Way Things Work was formative for me, and they just came out with a new edition. It's just simple, enjoyably-illustrated explanations of mechanics, simple machines, complex machines, electronics, etc.

I am assuming you're trying not to overly bias the responses, but there's obviously a lot of facts about this particular 11 year old that could very much change the recommendations. Without that context, I'm trying to think back to what I was reading at that age (in the late 90s, so not much new on my list, there may be better out there now), or what I wish I'd known to read at that age. I think at that age the thing I most enjoyed and most grew from were books that taught me how to play with concepts and ideas in a principled way in order to think about them in new contexts, as well as some history of science and math.

1. Any of the popular math books by Robert and Ellen Kaplan or Ian Stewart, including Ian Stewart's fiction. Things like The Art of the Infinite, or Flatterland.
2. Carl Sagan's Cosmos or The Dragons of Eden
3. Basically anything by Asimov. Also Terry Pratchett if the kid is more fantasy- than sci-fi- oriented (less science, but plenty of philosophy and reasoning about the implications of new and old ideas)
4. Alice in Wonderland if you include context about what Lewis Caroll was really talking about. Also The Phantom Tollbooth if they haven't read it yet. Even older classics like things by Jules Verne and HG Wells can be interesting choices. If the kid has only ever read more modern sci-fi and fantasy, it can be interesting to learn how people used to think about the future or other worlds. I personally really liked Last and First Men and Starmaker; I think I read those around the end of high school, but nothing in them was particularly advanced IIRC.
5. It might be a little early for Godel Escher Bach unless they're particularly into formal mathematics, but probably in another 2-3 years that's one to put on the list.
6. Plato and Aristotle. At this age the kid has technically been taught all the math and science needed to understand anything they wrote.
7. This one is more dependent on specific interests, but growing up I loved to cook, and lived in a house of people who loved to cook. For me, books like On Food and Cooking by Harold McGee (and later, The Food Lab by Kenji Lopez-Alt and Cooking for Geeks by Jeff Potter) were basically my introduction to organic chemistry. In my sister's words, for me, the kitchen is just another lab. They also helped build some very useful life skills.
8. Not sure if there's a specific reason for limiting to just books, but there's also some excellent youtube channels I'd recommend to such a kid. Veritasium, eigenchris, Vsauce, numberphile, Isaac Arthur, and even things like TierZoo can be great. Some of the videos may be a bit advanced for now, but just skip around and explore.
   1. Similarly, if they don't mind video games that look old and dated, I learned more from playing Sid Meier's Alpha Centauri than I did from almost any dozen books at that age. Apparently there is now an open source remake in progress?
9. This is also an "11 is probably too young for most" recommendation, there are some parts that are somewhat disturbing, but Ra by qntm (also available as a free online serial) is excellent but very weird. It has the hardest of hard magic systems. Like, literally, the word "mage" in story is "MagE" because they're a kind of engineer. There's even a whole appendix on why "make something invisible" is actually really complicated.
10. If they like literature and wordplay as well as more mathy technical stuff, Jasper Fforde's Thursday Next books are a lot of fun. Surprising density of math, philosophy, and sci-fi concepts for a series about jumping into classic novels. Good for sparking "Hey, what are they referencing here?" conversations.

GEB

Besides abstractapplic's excellent answer,

• A Brief History of Time and The Universe in a Nutshell by Stephen Hawking
• Ender's Game by Orson Scott Card
• Foundation by Isaac Asimov
• The Martian by Andy Weir
• Paleontology: A Brief History of Life by Ian Tattersall
• Richard Feynmann's books

I've just started my 11yr old tech minded son reading the Worm web serial by John Macrae (free and online, longer than Harry potter series).  It's a bit grim/dark and violent, but an amazing and compelling sci-fi meditation on superheroes and personal struggles.  A more brutal and sophisticated world build along lines of popular 'my hero academia' anime that my boys watched compulsively.  1000's of fanfics too.

Stories from Larry Niven's "known space" universe.  Lots of fun overcoming-challenges short stories and novellas that revolve around interesting physics or problems or ideas.  And the follow up Man-Kzin War series by various invited authors have some really great stories too with a strong martial bent that will likely appeal to most boys.

At that age I read and loved Dune, The stars my destination (aka Tiger Tiger, a sci fi riff on Comte de Monte Christo), Enders Game.  I think Terry Pratchett humor needs a more sophisticated adult knowledge base, with culture references that are dating badly.

My 11yr old loved the Expanse TV series, though I haven't given them the books to read yet and I can't recommend the transhumanism anime Pantheon on Amazon highly enough - its one of best sci fi series of all time.

All good to introduce more adult problems and thinking to kids in an exciting context.

Here is a category of book that I really loved at that age: non-embarrasing novels about how adults do stuff.  Since, for me, that age was in 1973, the particular books I name might be obsolete. There’s a series of novels by Arthur Hailey, with titles like “Hotel” and “Airport”, that are set inside the titular institutions, and follow people as they deal with problems and interact with each other.  And there is no, or at least minimal, sex, so they’re not icky to a kid.  They’re not idealized; there is a reasonable degree of fallibility, venality and scheming, but that is also fascinating.  And all the motivations, and the way the systems work, is clearly explained, so it can be understood by an unsophisticated reader.

These books were bestsellers back in the day, so you might be able to find a copy in the library.  See if he likes it!

Another novel in this vein is “The view from the fortieth floor”, which is about a badly managed magazine going bankrupt.  Doesn’t sound amazing, I know, but if you’re a kid, who’s never seen bad managers blunder into ineluctable financial doom, it’s really neat.

My wife is a middle school librarian.  I’ll ask her when I see her for more books like this.

Code by Charles Petzold. It gives a ground-up understanding of how computers actually work, starting slowly and without assuming any knowledge on the reader's part. It's basically a less textbooky alternative to The Elements of Computing Systems by Nisan and Schocken, which is great but probably a bit much for a young kid.

I re-read "I Robot" recently, and I don't think it's particularly good. A better Asimov is "The Gods Themselves" (but note that there is some degree of sexuality, though not of the sort I would say that an 11-year should be shielded from).

I'd also recommend "The Flying Sorcerers", by David Gerrold and Larry Niven. It helps if they've read some other science fiction (this is sf, not fantasy), in order to get the puns.

My 9yo has recently enjoyed Ender’s Game, Harry Potter, Hitchhiker’s Guide to the Galaxy, and What If. He recently asked to borrow my The Vital Question (it came up in conversation about abiogenesis) and he’s mostly following it so far but has occasional questions for me, we’ll see how far he gets or if he loses steam.

For non-books, he wanted to do Khan academy cosmology / astronomy, I think he did one big unit of Khan academy math before losing interest, he likes Eureka crates (little kits to build your own soap dispenser, rivet press, ukulele, whatever, they come once a month, good gift), lotsa video games, and he was doing DuoLingo Spanish every night (he has a streak, he’s a total sucker for gamification) but to my dismay decided to switch to the rather less practical DuoLingo Klingon. ¯\_(ツ)_/¯

Lewis Dartnell's The Knowledge - How to Rebuild Our World From Scratch is a sort of grand tour for technological underpinnings of industrial civilization and how you might bootstrap them. Might be a bit dry, but it's popular writing and if the kid's already reading encyclopedias it should fit right in. Lots of concrete details about specific technologies.

Might go for a left field option and see what he makes of Euclid's Elements.

Only one mention of Jules Verne in answers seems weird to me.

First and foremost, "The Mysterious Island". (But maybe it has already been read at nine?)