The old witch’s eyebrows rose. “How did he identify you to the Hogwarts wards, then?”
A slight smile. “ “The Headmaster drew a circle, and told Hogwarts that he who stood within was the Defense Professor. Speaking of which—”

Quirrell is Baba Yaga, a "she", and some "he" also in that circle is the Defense Professor. EDIT: The Troll is the Defense Professor.

Past Professors of Defense have included not just the legendary wandering hero Harold Shea but also the quote undying unquote Baba Yaga, yes, I see some of you are still shuddering at the sound of her name even though she’s been dead for six hundred years.

" quote undying unquote Baba Yaga"

Quote hint unquote.

“Here of course we have the Sorting Hat, I believe the two of you have met. It told me that it was never again to be placed on your head under any circumstances. You’re only the fourteenth student in history it’s said that about, Baba Yaga was another one

Gee, Baba Yaga's mind had the same effect on the Hat as Harry's. Do we hypothesize his brain being like anyone else's brain?

And I daresay that most wizards would be hard-pressed to name a single Dark Lady besides Baba Yaga.”

Yes, they'd be hard pressed to name a single Dark Lady besides Baba Yaga. Note how that doesn't say there weren't any, and indeed many. Maybe, let's say, the quote undying unquote Baba Yaga masquerading as other people? Do we know anyone else who masquerades as other people? Anyone else with a brain like Harry's?

I will say this much, Mr. Potter: You are already an Occlumens, and I think you will become a perfect Occlumens before long. Identity does not mean, to such as us, what it means to other people. Anyone we can imagine, we can be; and the true difference about you, Mr. Potter, is that you have an unusually good imagination. A playwright must contain his characters, he must be larger than them in order to enact them within his mind. To an actor or spy or politician, the limit of his own diameter is the limit of who he can pretend to be, the limit of which face he may wear as a mask. But for such as you and I, anyone we can imagine, we can be, in reality and not pretense.

There are 3 and only 3 mentions of Baba Yaga in the book so far, and they tie Harry, the Dark Lord, and Quirrell together.

“Oh, now I see!” said Tracey Davis, speaking up so suddenly that Hermione gave a small startle. “You’re joining our protest because you’re worried that not enough girls are becoming Dark Witches!”
There was a half-smile on Professor Quirrell’s face as he replied,...

Probably a good idea to pay close attention to what Quirrell says when he smiles to himself.

EDIT: Guess who else Harry is like?

“Congratulations indeed,” said Dumbledore. “Even I did not make any original discoveries in Transfiguration before the age of fourteen. Not since the day of Dorotea Senjak has any genius flowered so early.

Latest half baked idea. Harry is Quirrell. I'd been operating on the theory that Quirrell is preparing Harry to take over the world, and then take over Harry. He's actually already taken over Harry as a baby, and lived out a new life as Harry. There are multiple scense of Quirrell comparing events in his life to Harry's, with the implication that Harry's life is the new and improved one.

The whole "Sense of Doom" business is the potential coming together of one person in two time turned bodies in the same space time.

With the ridiculously rampant and specific foreshadowing, some kind of time turning solution seems likely. And causality back through time was already set up with the Comed-Tea incident

but it all makes sense once you draw the causal arrows going BACKWARDS IN TIME!”

Here's a fascinating quote by Dumbledore about Fawkes:

as close to undying as any creature that exists in this world, for whenever their bodies fail them they immolate themselves in a burst of fireand leave behind a hatchling, or sometimes an egg.”

And Harry is discovered as a baby next to the presumed immolated remains of Voldemort.