Step 1

Using electric mixer fitted with whisk attachment, beat together butter, salt, black pepper, and cayenne at low speed just until blended. Add Cheddar and flour and mix at low speed just until smooth (do not overmix). Shape dough into disk, wrap in plastic wrap or waxed paper, and chill 30 minutes.

Step 2

Arrange racks in upper and lower thirds of oven and preheat to 350°F. Line 2 large baking sheets with parchment paper.

Step 3

On lightly floured surface, roll out dough to 1/4- to 1/8-inch-thick round. Using 1 1/2- to 2-inch round cutter, cut out rounds and arrange 1 1/2 inches apart on baking sheets. Reroll scraps if desired (rerolled scraps will be tougher).

Step 4

Bake shortbread until lightly golden and beginning to brown on edges, about 13 to 15 minutes. Cool on sheets 5 minutes, then transfer to racks to cool completely.