Ah! A chef's coat! That changes things. You can still do the belly band, or you can turn that chef's coat into a concealed carry garment. It's not hard with basic sewing skills. There are small, cloth/elastic/soft nylon holster that are meant to be sewn in to a garment. Here's what you do.
Replace three buttons down the chest of your coat with snap buttons. Sew the original button on the outside of the coat to preserve its look. Then sew the holster inside the coat where you easily reach it but where it won't print. Then, holster your gun and button up. Should it need to be deployed, just yank the snaps with the left hand, reach in, then draw. Yes. It is a little work, but, if the jacket is a moisture repellent one that is moderately thick, that should be pretty comfy.
Compression shorts are tight, underwear-like shorts with a holster sewn on them. It keeps the gun pulled tight to the body inside your clothing. It might not be comfortable in a kitchen.