How did cooking begin?
Well I can only guess.
My thinking is that man without fire was eating all his food raw as nature served it up.
Then man discovered fire, probably from some lightening strike or volcanic activity.
Now there are 2 possibilities here, either at the scene of his discovery was also some unfortunate animal that got caught up in it. Man being an opportunist tries the heated/burnt/cooked meat and found it more tasty than raw. Secondly he took the fire home and at some point food accidentally ended up on the fire and same as first option he preferred the taste.
Simple answer: with the discovery of fire. Is very interesting the myth of Prometheus who stole fire from the gods for give it to humanity. Prometheus - Wikipedia