Combine the cheese, salt, pepper, and cayenne in a medium bowl and stir to combine. Add the butter. Using a hand mixer, beat the cheese mixture and butter until combined. Add the flour 1/4 cup at a time, mixing only until incorporated and the mixture holds together.
Place tablespoon-sized balls of the dough on 1 or 2 parchment paper-lined baking sheets, tapping the dough down gently with your fingertips. Bake until just beginning to brown at the edges, about 15 minutes. Let cool on the baking sheet for a few minutes. Transfer to a serving plate.