1. Heat oven to 350F. Have baking sheet(s) ready.
2. Knead together cookie dough and flour until completely blended. Roll out with a rolling pin to a scant 1/4 in. thick. Cut out cookies with cutters; reroll and cut scraps. Place about 1 in. apart on ungreased baking sheet(s).
3. Bake 8 to 12 minutes until golden. Transfer to a wire rack to cool.
4. To decorate cookies: Spoon 3/4 cup Royal Icing into a ziptop bag. Squeeze out air; seal bag. Using red food color, tint remaining icing pink. To thin pink icing for coating: Add water, 1 tsp at a time, until thin enough to spread.
5. To pipe border before coating (to keep thinned icing from flowing off cookies): Snip tip off corner of bag with icing. Pipe outline on cookies, saving some icing for words on cookies. Let dry about 5 minutes. To fill outlines: Dip brush in pink icing; spread to piped border. For sugared cookies: While pink icing is wet, sprinkle with colored sugar. Let dry completely, about 2 hours.
6. Pipe words on iced cookies with reserved unthinned icing.
In a large bowl, with mixer on low speed, beat 1 lb confectioners'' sugar and 3 Tbsp Just Whites (powdered egg whites) until combined. Add 6 Tbsp water; beat until blended. Increase mixer speed to high and beat 8 minutes or until icing is very thick and white. Makes about 21/2 cups.
Can be made up to 1 week ahead. Store loosely covered in a cool, dry place with wax paper between layers.