Neanderthal Stew

Uncooked meat tends to be chewey so some studies suggest cooking was the way that improved protein intake for the brain to grow, plus being able to make it easier to digest.

So one reason that modern humans might have had an advantage over the Neanderthals might be the ability to cook the food they killed or gathered.

Which bring us to this article at Archeology.com

Analysis of individual amino acids in collagen from an array of bones found at two sites in Belgium suggests that the Neanderthals' diet differed from that of other predators....the Neanderthals primarily specialized on the large plant-eaters such as mammoths and woolly rhinoceroses,”
... The study also revealed that about 20 percent of the Neanderthal diet came from vegetarian sources. “We are accumulating more and more evidence that diet was not a decisive factor in why the Neanderthals had to make room for modern humans...

uh, maybe it was cooking? there is a debate if Neanderthals cooked their foods.

from LiveScience:

While some fossil sites suggest Neanderthals used fire, they may not have used it often or consistently. For instance, Neanderthals occupied two sites in southwest France — Roc de Marsal, and Pech de l'Aze IV — for tens of thousands of years. The sites contain tens of thousands of stone tools and animal bones, but almost no evidence of fire making, said Dennis Sandgathe, an archaeologist at Simon Fraser University who has excavated the sites.

on the other hand, NatGeo Article claims they not only had fire to roast the food, but could boil it

based on evidence from ancient bones, spears, and porridge, Speth believes our Stone Age cousins likely boiled their food. He suggests that Neanderthals boiled using only a skin bag or a birch bark tray by relying on a trick of chemistry: Water will boil at a temperature below the ignition point of almost any container, even flammable bark or hides.

 , which is one step up from simple cooking or roasting, because it implies the ability to visualize a container and visualize that this container could be used to cook, and then figuring out how to do it: not only to make pots, but the knowledge that if you put a stone into a pot of water it will boil if you do it right).

so what is the evidence? The NatGeo article says thhere is no direct evidence, but two suggestions make the theory possible: One, the Neanderthals made glue from birch bark, and two, bones showed no scraping or gnaw marks, suggesting the meat was softened by cooking before it was removed from the bone.

the Museum of Natural History article discusses the diet suggested by teeth tartar.

They found evidence of grass seeds like wheat and barley, legumes, and even date palm fruit. Henry and her colleagues also noticed an interesting trend in some of the starches – while they could identify most of the fossils in the dental calculus samples, some of the starch microfossils they found appeared to be distorted.

distorted as in "having been cooked". But no information if it was just toasted, or was it boiled, or was it ground into flour and mixed with water before being cooked?

Which bring us to the next question: Did Neanderthals brew beer? Answer: Probably not...