In large bowl, beat sugar and margarine until light and fluffy. Add milk, vanilla and egg; blend well. Lightly spoon flour into measuring cup; level off. Stir in flour, cocoa, baking powder and baking soda; mix well. Cover with plastic wrap; refrigerate 1 hour for easier handling.
Heat oven to 350°F. On lightly floured surface, roll out dough, 1/3 at a time, to 1/8-inch thickness; refrigerate remaining dough. Cut with floured 2 1/2-inch star-shaped cookie cutter. Using drinking straw, punch random holes in cutout stars. Place 2 inches apart on ungreased cookie sheets.
Bake at 350°F. for 8 to 11 minutes or until set. Immediately remove from cookie sheets. Cool completely. Sprinkle with powdered sugar.