Preheat oven to 450 degrees F (230 degrees C). Lightly grease a baking sheet.
Mix flour, baking powder, 3/4 teaspoon garlic powder, salt, and white pepper together in a bowl.
Cut shortening into flour mixture with a knife or pastry blender until the mixture is slightly lumpy. Stir milk, Cheddar cheese, and pepperoni into flour mixture until well blended. Drop 2-inch balls onto the prepared baking sheet.
Bake in the preheated oven until golden, 12 to 15 minutes.
Stir butter and remaining 1/2 teaspoon garlic powder together in a small bowl; brush onto biscuits.