From the Super Mario Wiki
Cheesy Drumsticks are consumables that can only be used by Bowser in Mario & Luigi: Bowser's Inside Story + Bowser Jr.'s Journey, partially replacing Star Candies from the original game. They are the strongest type of drumstick that was added in the remake, surpassing the TNT Drumsticks. If eaten, Bowser instantly recovers all HP and BP, so it can be seen as Bowser's equivalent to the Star Candy, which can only be used by Mario and Luigi. The player can also purchase Cheesy Drumsticks near the end of the game.