Hello, u/Adhiraj and I independently did some research and the only good source of methionine we found is brazil nuts, which of course you probably don't want to eat much of since they can give you selenium poisoning.
The conventional wisdom is to just eat more protein to compensate for the poor amino acid balance, but you're going to be eating a lot, so I prefer to supplement methionine.
I have adding methionine in meals I cook and adding it to the plant based protein powder I use, precisely measuring how much I add. You can get individual amino acid supplements from iHerb and some larger health food shops.
Some sources of vegan protein go much much farther doing this (e.g. red lentils). I tend to eat soy TVP which goes somewhat further with methionine supplementation.
I also have a pure EAA protein powder which is entirely fermented and have a balanced amino acid profile. These are generally very poorly marketed supplements but they are widely available.
There's no need to add it to your food rather than mix it in a drink, other than you probably want to get all your amino acids around the same time, and it helps if you're doing meal prep and you don't need to work out how much to supplement every time you go to eat.
There is apparently research suggesting that too much methionine can increase the risk of type 1 diabetes. I'm not going to go into that, but it makes sense to err on the side of not over-supplementing methionine.
We have been use this tool to help work out the amount of methionine we need to supplement, but it's not a pleasant user experience: https://tools.myfooddata.com/protein-calculator
This is just my quick answer from memory, I may do a full writeup later.
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Non-animal based protein sources mostly have a different amino acid profile than animal-based protein sources. Different plants also have a different composition.
From looking a bit at the data myself it seems that if you mix different plant protein sources, you can get a good balance for most amino acids with the expectation of Methionine.
Mike from Renaissance Periodization who's a professor of exercise science suggests that a vegan can just look at the Protein digestibility-corrected amino acid score (PDCAAS) and use this as a factor for protein consumption to get the correct amino acid consumption as a vegan.
From thinking about the issue myself, I would expect that you get significantly lower Methionine consumption if you do that then a person who uses animal-based products as their protein sources.
Given that a protein needs a very exact number of each amino acid to be synthesized, for essential amino acids like Methionine, I would expect their consumptions to be a bottleneck for muscle building which needs protein. Even if all the other proteins are in good amounts and thus the PDCAAS score is decent, you can drown in a river that's on average 20cm deep.
One possible solution would be to focus on high Methionine protein sources as a vegan and less on the PDCAAS (for a vegan protein source, soy is good at both) and just consume twice the amount of protein that a non-vegan would to get similar Methionine consumption. I'm not sure what the exact consequences of having all the other amino acids in excess happen to be.
Has someone thought more about this and come to a good conclusion about how to think about Methionine as someone with a mostly vegan diet who wants to build muscle?