Beat butter at medium speed with an electric mixer until creamy; gradually add sugar, beating well.
Combine flour, baking powder, and salt; add to butter mixture, beating at low speed until blended.
Turn dough out onto a lightly floured surface; roll to 1/8-inch thickness. Cut with a floured 3-inch round cutter, and place 1 inch apart on parchment paper-lined baking sheets.
Bake at 300° for 20 minutes or until edges are lightly browned; remove to wire racks to cool.
Chocolate Shortbread Cookies: Reduce flour to 3 1/3 cups. Add 2/3 cup cocoa to flour mixture, and proceed as directed.