As human ancestor diet changed to calorie rich food their brains tripled in size

https://www.scientificamerican.com/article/food-for-thought-was-cooking-a-pivotal-step-in-human-evolution/
https://www.nature.com/articles/543592d.pdf
http://www.bbc.com/earth/story/20170327-why-our-brains-grew-so-big
https://www.smithsonianmag.com/science-nature/why-fire-makes-us-human-72989884/?page=1
https://www.scientificamerican.com/article/cooking-up-bigger-brains/
http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0100-84551997000100023
http://kreativproces.dk/http:/kreativproces.dk/wp-content/uploads/2010/08/Dunbars-tal-og-reseach.pdf
http://rstb.royalsocietypublishing.org/content/royptb/372/1727/20160244.full.pdf
https://sydney.edu.au/news-opinion/news/2015/08/10/starchy-carbs--not-a-paleo-diet--advanced-the-human-race.html
Humans are known for sporting big brains. On average, the size of primates' brains is nearly double what is expected for mammals of the same body size. Across nearly seven million years, the human brain has tripled in size, with most of this growth occurring in the past two million years.

Originally, large brains were thought to be essential for the making of stone tools, and this is why Homo habilis (skillful man) was thought to be the start of our Homo genus some 2.5m years ago. But we now know that many other animals make and use tools. We also know hominins living 3.3m years ago were already using stone tools half a million years before Homo evolved. 

So why did we evolve a large brain if it wasn’t essential for tool making? One theory is that existing in a large social group is very mentally taxing. Those who are better at playing the social game will have more access to mates and resources and will be more likely to reproduce. As the groups get larger, so the computational power needed to keep up with the interconnections grows exponentially, as does the stress. This theory of brain evolution was the social brain hypothesis is an internal arms race to develop the higher cognitive skills to enable greater social control.

For the first two thirds of our history, the size of our ancestors' brains was within the range of those of other apes living today. The species of the famous Lucy fossil, Australopithecus afarensis, had skulls with internal volumes of between 400 and 550 millilitres, whereas chimpanzee skulls hold around 400 ml and gorillas between 500 and 700 ml. During this time, Australopithecine brains started to show subtle changes in structure and shape as compared with apes:

The human brain requires 20-25 percent of a human’s energy even though it accounts for only 2% of body mass; by comparison, an ape’s brain requires only 8 percent of the energy. This means that from the time of H. erectus, the human body has depended on a diet of energy-dense food.

To evolve the hunter and gathers had to find significant additional energy required for the brain to function. See below the number of hours a primate must spend eating raw foods to sustain body and brain:

Chewing raw food  is slow and our ancestors needed many hours a day to fullfill their daily energy needs. When H. erectus was not hunting and gathering food, it would literally be chewing that food for the rest of the day. Cooking saves energy as cooked food is much faster to consume and expends less digestive effort breaking down cooked food than raw.

Even today there is evidence that people on raw food diet consume fewer calories and have lower BMI/weight:

Harvard primatologist Richard Wrangham, argues that the biggest revolution in the human diet came not when we started to eat meat but when we learned to cook. Our human ancestors who began cooking sometime between 1.8 million and 400,000 years ago probably had more children who thrived, Wrangham says. Pounding and heating food 
“predigests” it, so our guts spend less energy breaking it down, absorb more than if the food were raw, and thus extract more fuel for our brains. “Cooking produces soft, energy-rich foods,” says Wrangham. Today we can’t survive on raw, unprocessed food alone, he says. We have evolved to depend upon cooked food.

To test his ideas, Wrangham and his students fed raw and cooked food to rats and mice. In Wrangham’s lab at Harvard, his then graduate student, Rachel Carmody, opened the door of a small refrigerator to show  plastic bags filled with meat and sweet potatoes, some raw and some cooked. Mice raised on cooked foods gained 15 to 40 percent more weight than mice raised only on raw food.

Prehistoric humans ate some meat but it didn’t make them smart. Humans evolved when they used fire for cooking, they ate and cooked richer food, worked together to hunt and forage, gave more food to females with children, and used their growing intellect to stabilise their supplies. This evolution went on for two million years. Brain evolution was due to high quality diet, yet this does not need an increased proportion of animal based products. 

As human ancestor evolved and started consuming calorie dense, predigested foods they changed in to significant ways:

• The size of the gastro-intestinal tract is dependent on both body size and the quality of the diet. As humans started cooking food their gut reduced in size.
• Brain grew larger

Neurons power the brain and use twice the energy as any other cell type in the body, run almost exclusively on glucose from carbohydrate.  Moreover, because neurons aren't able to store glucose as glycogen as other cells in the body do, they must receive glucose in constant supply.  

Peter Ungar, distinguished professor and chair of anthropology at University of Arkansas, wrote "Even the staunchest meat advocates recognize that protein and fat cannot power the brain – and we lose much of our gluconeogenesis capabilities at weaning. The argument is that meat eating provided the calories needed to power other parts of the body, freeing available carbohydrates to focus on the brain… Even in that case, it’s carbs, not meat that powers the brain".
If Wrangham is right, cooking not only gave early humans the energy they needed to build bigger brains but also helped them get more calories from food so that they could gain weight.