Beat butter or margarine and shortening in a large mixing bowl with an electric mixer on medium to high speed for 30 seconds. Add sugar, baking powder, and salt; beat until combined, scraping sides of bowl occasionally. Beat in egg and 1 teaspoon vanilla until combined. Beat in as much of the flour as you can with the mixer. Stir in remaining flour with a wooden spoon. Streak dough with food coloring. Place dough in a plastic bag and knead until dough is lightly marbled. Add more coloring, if necessary. Divide dough in half. Cover and chill for 3 hours or until easy to handle.
Roll each half of dough on a lightly floured surface until 1/8 inch thick. Cut with a floured egg-shape cookie cutter. Place cutouts on an ungreased baking sheet.
Bake in a 375 degree F oven for 7 to 8 minutes or until edges are firm and bottoms are very lightly browned. Transfer to wire racks and cool.
If desired, stir together powdered sugar, 1/4 teaspoon vanilla, and the milk in a small mixing bowl. Stir in additional milk, 1 teaspoon at a time, until icing is smooth and of piping consistency. Use icing to pipe stripes or other design on cooled cookies. Makes 36 to 48 eggs.