Preheat your oven to 350°F. Line a baking sheet with parchment paper.
In a mixing bowl, combine the flour, baking powder, and salt.
In another bowl, cream together the softened butter and shredded cheddar cheese until well blended.
Gradually add the dry ingredients to the cheese mixture, mixing until a dough forms.
Stir in the garlic powder, onion powder, and black pepper.
Roll the dough into small balls, about 1 inch in diameter, and place them on the prepared baking sheet, spacing them about 2 inches apart.
Brush the tops of the cheese bites with the beaten egg for a golden finish.
Bake in the preheated oven for 15-20 minutes or until the bites are golden brown.
Allow to cool slightly before serving.