Preheat oven to 350 degrees. Combine the flour, cayenne, and salt in a large shallow bowl. With a pastry blender, cut in the butter until the mixture is the texture of coarse meal. Add the cheese and rub into the flour-butter mixture gently with your fingertips until a small bit of dough, when pinched together, will hold its shape. Roll into 3/4-inch balls, place 1 1/2 inches apart on ungreased baking sheets, then flatten into rounds 1/4-inch thick by pressing with a flat-bottomed glass that has been dipped into flour. (You'll have to keep dipping the glass into flour to keep the dough from sticking to it.) Bake uncovered 10 to 12 minutes until pale tan. Transfer the wafers at once to wire racks to cool, then store airtight.