Beat butter with sugar until smooth and creamy. Add egg and extracts. Beat well. Whisk flour with baking powder and salt until very well blended, then gradually blend into creamed mixture to form a smooth dough.

Divide dough in half. Blend green coloring and green cherries into one half, and red coloring and red cherries into the other half. Wrap each ball of dough separately in plastic and chill well, at least one hour.

Roll each color dough between sheets of waxed paper to form two 9x12" rectangles. Remove top layers of waxed paper and flip the green rectangle evenly on top of the pink rectangle. Peel away top sheet of waxed paper and roll dough up jellyroll fashion beginning on the 12-inch side of the rectangle.

Tightly wrap rolled "pinwheel log" into waxed paper and chill again until firm, at least one hour or overnight. Dough can be held about a week in the refrigerator at this stage or up to a month in the freezer.

To bake, preheat oven to 350°F. Remove waxed paper and slice dough into 1/4-inch rounds. Place 1 inch apart on ungreased baking sheets and bake in the oven's center for 10-12 minutes, or until edges just become golden. Cool on baking sheets 1-2 minutes to firm up slightly, then quickly move cookies to a rack to complete cooling. Store cooled cookies in an airtight container at room temperature. Recipe yields about 4 dozen cookies.