Beat butter at medium speed with an electric mixer until creamy. Add sugar, beating until light and fluffy. Add egg and vanilla, beating until blended. Gradually add flour, baking powder, and salt, beating until blended.
Divide dough into thirds; place each portion in a separate bowl. Stir chocolate and walnuts into 1 portion; chopped cherries and red food coloring into second portion; and coconut and rum extract into third portion.
Line an 8-inch square baking dish with plastic wrap. Press chocolate mixture into dish. Top with rum mixture and cherry mixture, pressing gently. Cover and chill 8 hours.
Cut dough evenly into 5 sections. Cut each section into 1/8-inch-thick slices. Arrange slices, 2 inches apart, on ungreased baking sheets.
Bake at 375° for 8 to 10 minutes or until lightly browned. Remove to wire racks to cool. Freeze up to 1 month, if desired.