Unwrap the mozzarella sticks and place them on a baking sheet. Freeze for at least 60 minutes.
Set up three shallow bowls: one with flour, one with the beaten eggs, and one with the crushed Cheetos.
Dredge each frozen mozzarella stick in flour, shaking off excess. Dip into the beaten eggs, then roll in the crushed Cheetos, pressing gently to adhere. For a thicker coating, repeat the egg and Cheetos steps.
Place the coated mozzarella sticks back into the freezer for 15 minutes to set.
Preheat the oven to 400°F.
Bake for 7 to 10 minutes, keeping a close eye to prevent the cheese from oozing out. Serve with your preferred dipping sauce.