We have brothers, the big one is a popcorn fiend and the other will eat bread if you leave it in his reach, through the bag even. Carrots too, acts like they're catnip.
I’ve had a carrot cat too! I sliced some up and dehydrated them then sewed them into a toy and she just loved it! The trick I found is to break the pieces inside the toy now and then to release more of the smell (same way catnip works really).
Does your carrot cat also like swimwear that’s been used in a chlorinated pool, but not yet washed? Mine treated that like catnip, too.
One of my orange, but non-carrot loving, cat is definitely a fiend for unwashed chlorinated swimwear. Like you mentioned, treats it like catnip (which he also fiends over) he used to really like ice cubes too but eventually seemed to stop caring.
He also loves cheese... Found out parmesean doesn't give him issues but mozzarella did.
One of our cats loved salady stuff, cucumbers, sweetcorn and bell peppers especially.
He was never possessive over food, not even tuna, except for red bell peppers, - the only time we heard him growl at his brother was whenever we gave him a few pieces.