1. Cut butter into chunks and put in a large bowl; add sugar. Beat with a mixer to blend, then beat on high speed until mixture is fluffy.
2. Add whole egg and vanilla and beat to mix thoroughly.
3. Add 3 cups flour and beat on low speed until dough is well mixed.
4. Divide dough in half, shape into balls, and flatten each into a round cake. If desired, wrap dough airtight and chill up to 1 day.
5. One portion at a time, roll out dough on a floured board to 1/4 inch thick. With flour-dusted cookie cutters (2 to 3 in. wide), cut out cookies.
6. With a wide spatula, transfer cookies to baking sheets, spacing them at least 1 inch apart.
7. To make patterns on cookies, if desired, make impressions with a flour-dusted spoon tip or fork tines. Gently brush flour off cookies.
8. Mix egg yolk with 1/2 teaspoon water to blend. Divide mixture among 4 small bowls. Tint contents of each bowl with a different food coloring, mixing in a drop at a time to get desired intensity.
9. Using small brushes, paint surface of cookies with colored mixtures.
10. Bake in a 325° oven until cookies are golden on bottom, about 16 minutes (if using one oven, alternate pan positions after 8 minutes). Cool on pan about 5 minutes, then transfer with a wide spatula to racks to cool.
11. Serve, or store airtight at once for up to 5 days. Freeze to store longer.
Nutritional analysis per cookie.