Preheat the oven to 425 degrees F.

Whisk together the flour, baking powder, and salt in a large bowl. Cut in the chilled butter pieces using a pastry cutter until the mixture becomes a mealy texture.

Add in the cheese and cayenne pepper and mix until well blended. Pour in the milk and stir until the dough is soft. You might need to add a little more milk to ensure the dough is completely wet.

Remove the dough to a lightly floured work surface and knead it gently a few times.

Pat the dough out into a circle about 1/2-inch thick. Cut out rounds using a 2 1/2-inch biscuit cutter.  Work the scraps together and cut additional rounds.

Place the rounds on an ungreased baking sheet about 1/2-inch apart.

Bake in the upper third of the oven until the biscuits are golden brown. This will take about 12 to 13 minutes. Serve them while they are hot, or at room temperature.