In a small bowl, beat egg and water.
Place panko, Italian seasoning, and pepper in separate dishes.
Coat cheese sticks in flour, then dip in egg mixture and the 3 bowls.
Cover and chill for at least 4 hours.
Place on an ungreased baking sheet and bake, uncovered, at 450°F for 5 minutes, until warm, then run under the broiler quickly to brown.
Cool before serving. Serve with snap peas.