From appearances, and the way he constantly fishes pieces out of his mouth and puts them on his plate and picks his teeth, and also according to online sources (like here and here), it's a horrible, cold piece of leftover steak which he was eating before he passed out drunk. Unfortunately, it doesn't appear to be in the script, where circumstances are a bit different (there are a couple of ladies with him there).
Director Paul Thomas Anderson confirmed this in an interview (around 5:18):
INTERVIEWER: Did you intentionally leave food out of the movie, for the most part? And the food that's in it is so unappetizing.
ANDERSON: Not really intentionally, no. I mean, there was actually one scene that we cut out that caught Daniel sort of mid-bite, he was having a steak. And we cut it out, but we had to decide if Daniel was going to be doing anything in that last scene in the bowling alley, and I suggested that he be gnawing on a piece of steak, or at least what he could kind of get the nutrients of, considering his teeth had probably fallen out, you know, just suck on a steak. I knew it was a tall order because to do take after take of gnawing on a steak, you know, is really dangerous ground to get into, and Daniel [Day-Lewis] went away for a few days and thought about it and said, "Alright, let's do the steak. That's a good idea".
Well, I guess steak is answer, right from the horses mouth... but it doesn't look like a steak, whatever it is that Daniel Day Lewis is actually eating. For the character of a toothless man, Daniel seems to be extracting enormous bites out of it, whatever it is. I was under the impression that it was a giant 1920's version of a Kit-Kat. A semi-soft chocolate pastry.
So, what is it, really? Not 'what is the character eating', now that it's confirmed to be a horrible leftover steak (what's so horrible about last nights steak, anyway? Were leftovers generally accepted as horrible in the 1920's, or is that somebody's personal opinion now? I'd like to know), but what is Daniel Day Lewis actually picking up, masticating and swallowing? What is it? What is that chocolate looking, semi-pastry seeming meat imposter?
If I were to go out on a limb here, I'd say that it's a McRib patty thing. Soy meat, in generic terms.
Shortly after Daniel says "I drink your water; I drink it, every day", you clearly see a piece of bitten-off steak in his right hand...