1. Preheat the oven to 350 degrees F. Line 2 baking sheets with parchment paper.
2. Roll the chilled dough into 1 1/4-inch balls, and place on the prepared baking sheets, about 2 inches apart. Bake 9 to 11 minutes or until edges are lightly golden brown. Transfer to a wire rack to cool completely.
3. To make the Royal Icing, in a medium bowl combine the powdered sugar, dried egg whites and water. Beat with an electric mixer on low speed until blended. Increase the speed to high and beat until smooth and thick.
4. Divide the royal icing into smaller bowls. Tint 1 cup of the icing with the cocoa, adding additional water as needed to reach a thin piping consistency. Tint remaining icing as desired with food coloring.
5. Arrange the cookies on a wire rack over a piece of parchment paper. Place each color in a zip-top bag. Press out the excess air and seal the bags. Snip a very small corner from each bag, and pipe onto the cookies. Let cookies stand until icing is set, about 1 hour.
1. In a medium bowl combine the flour, baking soda, and salt.
2. In a separate large bowl beat the butter and sugars with an electric mixer until light and fluffy, about 2 minutes. Add the eggs, one at a time, beating well after each addition. Beat in the vanilla. Gradually add the flour mixture, beating until just combined.
3. Divide the dough in half, and proceed with a cookie recipe. (Each recipe uses half of the Basic Recipe.) To save the dough for later use, shape each half into a disc, wrap in plastic, and freeze for up to a month.