In a large bowl, cream the butter and sugar together until the mixture is light and fluffy. Beat in the egg, vanilla extract, and almond extract.
In a separate bowl, whisk together the flour, baking powder, and salt. Gradually add this dry mixture to the creamed mixture, beating well to combine.
Divide the dough into three equal portions. Tint one portion with the red food coloring, another with the green food coloring, and leave the third portion plain.
Roll out each portion between sheets of waxed paper into a 9 by 6-inch rectangle. Refrigerate the rolled dough for 30 minutes.
Remove the waxed paper and layer the dough portions in the order of red, plain, and then green.
Roll the layered dough tightly into a jelly-roll shape, starting from one of the long sides. Wrap the roll in plastic wrap and refrigerate for 2 hours or until firm.
Preheat the oven to 375 degrees Fahrenheit. Unwrap the dough and cut it into 1/4-inch slices for pinwheels or checkerboard shapes. Place the slices 1 inch apart on ungreased baking sheets.
Bake for 9 to 11 minutes or until the cookies are set. Remove from the oven and allow to cool on wire racks.