Preheat a toaster oven on broil setting, or set an oven rack about 6 inches from the heat source and preheat the oven's broiler. Spray a small baking sheet with cooking spray.
Insert toothpick vertically into each cheese stick half to mid-way point. Beat egg in a small bowl. Place bread crumbs in a separate small bowl.
Dip each cheese stick into egg, then press into bread crumbs. Repeat dipping in egg and breadcrumbs for a double-thick coating. Place cheese sticks on prepared baking sheet and spray with additional cooking spray for uniform browning.
Broil in preheated oven until golden brown, 4 to 5 minutes. Allow cheese sticks to set before serving, about 1 minute.