Preheat your oven to 375°F. Line a baking sheet with parchment paper.
In a medium bowl, whisk together the flour, baking powder, salt, black pepper, and garlic powder.
In a large bowl, beat the softened butter until creamy. Add the shredded cheddar cheese, egg, and Dijon mustard. Mix until well combined.
Gradually add the dry ingredients to the cheese mixture, stirring until a dough forms. If using cayenne pepper, fold it in at this stage.
Using a tablespoon, scoop out portions of the dough and roll them into balls. Place the balls on the prepared baking sheet, spacing them about 2 inches apart.
Bake for 15-18 minutes or until the bites are golden brown. Remove from the oven and let them cool for a few minutes on the baking sheet before transferring to a wire rack.
Serve warm or at room temperature.