In a large mixing bowl, beat butter with an electric mixer for 30 seconds. Add sugar, baking powder and salt. Beat until combined, scraping sides of bowl occasionally. Beat in the egg and vanilla until combined. Beat in as much of the flour as you can with the mixer. Stir in any remaining flour with a wooden spoon. Divide dough in half.
Combine coffee powder and water. Knead into one portion of dough. Shape each dough portion into a rectangular log that is about 6 inches long and 2 inches wide. Wrap logs in waxed paper or plastic wrap and chill for 1 hour. With a sharp knife, cut each log lengthwise into four slices. Alternating colors, stack the slices to form two four-layer logs. Press dough together to seal layers. Wrap logs in waxed paper or plastic wrap, and chill for 30 to 60 minutes or until firm.
Place logs on a cutting surface with a solid color facing up. Using a sharp knife, cut each log lengthwise into four slices. (Each will have four layers in alternating colors.) Stack four slices of dough, alternating colors for a checkerboard effect. Repeat with remaining slices for second log. Trim edges to straighten. Wrap and chill for 1 to 2 hours or until firm.
Cut each log crosswise into 1/4-inch-thick slices. Place slices 2 inches apart on ungreased cookie sheets. Bake in 375 degree oven for 10 to 12 minutes or until edges are lightly browned. Transfer cookies to wire racks and let cool. Makes about 48 cookies.