Dip cheese stick halves into egg and roll in bread crumbs to completely coat the sticks; place breaded cheese sticks onto the prepared baking sheet. Allow cheese sticks to stand at room temperature for about 5 minutes to set, and repeat dipping in egg and bread crumbs to form a thick coating. Freeze breaded cheese sticks for at least 2 hours.
Heat oil in a deep-fryer or large saucepan to 350 degrees F (175 degrees C