Slice cheese into bars. In a shallow dish, whisk eggs and milk together. Place flour into another shallow dish. Place breadcrumbs into the last shallow dish.
Dip each cheese stick into the egg mixture, then coat in flour, back into eggs, and roll in the breadcrumbs. Set onto a plate and freeze for at least one hour. Preheat air-fryer to 375 F. Air-fry cheese sticks in batches for 10-12 minutes.