Beat butter at medium speed with a heavy-duty stand mixer until fluffy. Gradually add flour, salt, and red pepper, beating just until combined. (Mixture will be crumbly.) Add cheese and tapenade, beating at low speed just until combined.
Roll dough into 2 (10-inch) logs, using plastic wrap to shape dough. Wrap each in plastic wrap, and freeze at least 1 hour. Cut each log into 1/4-inch-thick slices, and place on parchment paper-lined baking sheets.
Bake at 350° for 15 to 18 minutes or until lightly browned. Cool 5 minutes on pan; remove from pan to a wire rack, and cool 30 minutes or until completely cool.
Note: Shortbread dough can be frozen up to 1 week; just allow it to stand at room temperature 5 to 10 minutes before slicing.