Beat butter at medium speed with an electric mixer until creamy; gradually add cheese, beating well. Combine flour, salt, and red pepper; gradually add to cheese mixture, beating well.
Shape dough into 1/2-inch balls; place on ungreased baking sheets. Press a pecan half into each ball to flatten.
Bake at 350° for 12 to 15 minutes. Cool 5 minutes; transfer to a wire rack to cool completely.
Note: For testing purposes only, we used Kraft Sharp Cheddar Cheese.