Beat butter at medium speed with an electric mixer until creamy; gradually add sugar, beating well.
Stir together Kahlúa, coffee granules, and vanilla until coffee dissolves; add to butter mixture, beating until blended.
Combine flour, baking powder, and salt; add to butter mixture, beating at low speed just until blended.
Turn dough out onto a lightly floured surface, and roll to 1/8-inch thickness. Cut with a floured 3-inch round cutter, and place 1 inch apart on lightly greased baking sheets.
Bake at 375° for 7 minutes or until cookies are lightly browned; remove to wire racks to cool.