He's a chef. He has to be eating something at work as well as eating at home. Has he changed jobs and so changed the type of food he tastes at his restaurant? Does he drink alcohol and has his pattern of drinking changed (type of drink, frequency)?
Has he tracked his food, put it in a log in accurate quantities and shown that to his doctor (a week's worth, for example). Even if he's eating more, that doesn't explain the suddenness of this change. When the change occurred, what else was going on? Did he stop smoking around that time, for example?
What happens when he fasts, for a day, for example? Can his doctor give him a referral to a dietician? Perhaps also a hormone specialist?
The reason medical people harp so much on the calorie side of things is that the smoke usually points to that fire. Maybe your boyfriend does have Cushing's. I hope not, but at least you two would know the explanation for this big change in his body.
My doctor recently ordered a lot of blood tests while I was waiting for an appointment with a specialist. I asked for the blood tests because I said I didn't want to waste time if there was another answer to be found. I wanted to see the specialist with the background knowledge of the results of those tests. Wow, was it expensive! The specialist didn't even ask me about those tests. At least I know. But it was costly - and ended up in the 'deductible' of my insurance. Oh, well.