In a bowl, cream together 1 1/2 cups confectioner's sugar, granulated sugar and butter, then mix in the egg and vanilla and almond extracts. In another bowl, stir together the flour, baking soda, and cream of tartar; mix the dry ingredients into the creamed mixture, then cover and refrigerate for 2 to 3 hours, or overnight.
Preheat the oven to 350 °F.
Divide the chilled dough in half and roll it out on a lightly floured pastry cloth to a 1/4-inch thickness. Lightly grease some baking sheets. Cut the dough with a floured cookie cutter; sprinkle with sugar. Transfer the cookies to the prepared sheets and bake for 9 minutes.
In a medium bowl, combine egg whites, 1 box confectioner's sugar, and cream of tartar. Beat at low speed with an electric mixer until blended. Increase mixer speed to high, and beat 8 to 10 minutes, or until mixture holds a peak. Cover with a damp cloth when not in use. Separate into bowls and add food coloring, if desired.