"I read a newspaper while he cooks."

Lagar is almost never alone when referring to food. In swedish one does not just cook, one is either cooking some specific food, like lagar ett ägg, or cooking (food) in general, lagar mat

Kockar means 'chefs'

I think (not very sure) that you can also say for example: "Jag lagar kyckling". I think is correct too.