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1. In a medium mixing bowl stir together flour and baking powder; set aside. In a large mixing bowl beat butter with an electric mixer on medium to high speed for 30 seconds. Add the 1 cup sugar; beat until fluffy. Add egg, vanilla, and extract; beat well. Add flour mixture; beat until well-mixed. Divide dough into three equal portions. Stir red food coloring into one portion, stir green food coloring into another, and leave remaining dough portion plain. Cover; chill about 1 hour or until dough is easy to handle.
2. Preheat oven to 375 degrees F. Divide each color of dough into four equal portions. On a lightly floured surface, roll each portion into a 1/2-inch-diameter rope. Place one red, one green, and one plain rope side by side. Twist together. Repeat with remaining ropes. Chill dough for 30 minutes. Cut ropes into 1/2-inch-thick slices for larger cookies or 1/4-inch-thick slices for smaller ones. Carefully roll slices into balls, blending colors as little as possible. Place about 2 inches apart on ungreased cookie sheets. Using the bottom of a glass dipped in sugar, flatten each ball to 1/4-inch thickness.
3. Bake in preheated oven until edges are set (allow 8 to 10 minutes for larger cookies; 6 to 8 minutes for smaller ones). Transfer cookies to wire racks; cool. Makes about 72 (2-1/2-inch) or 144 (1-1/4-inch) cookies.