"Cook food" is an objective in the quest The Hunger Pangs in The Horrible Hunger of the Ravenous Wattle Gobbler DLC
The food will start cooking and a gauge will appear below "Cook Food". You need to defend the oven against the Chefs that President Smith sent against you. They are trying to shut down the oven and you just need to defend it. All you need to do is stay near the button and they will all come to you.
The head chef of this group is Chef Bork Bork. Kill him and keep defending the food until it is done.