Step 1

In the bowl of a stand mixer fitted with a paddle attachment, beat the butter and sugar on medium speed until creamy, 3 to 4 minutes. Using a rubber spatula, scrape the bottom and sides of the bowl. Add the egg yolks and vanilla, then mix on low until fully combined, scraping the bottom and sides of the bowl as needed.

Step 2

In a medium bowl, whisk together the flour, baking powder, salt, and nutmeg.

Step 3

With the mixer on low speed, gradually add the flour mixture to the butter mixture, alternating with the eggnog, beginning and ending with the flour mixture, beating just until combined after each addition.

Step 4

On a lightly floured work surface, place the dough. Divide the dough in half and form into disks. Wrap each disk in plastic wrap and refrigerate until firm, 30 minutes to 1 hour.

Step 5

Place one oven rack in the upper third of the oven and a second oven rack in the lower third of the oven. Preheat the oven to 350°F. Line 2 baking sheets with parchment paper.

Step 6

Working with 1 disk of dough at a time and keeping the second disk refrigerated, lightly flour a work surface. Roll the dough out until ¼-inch thick. Use a 2- to 3-inch cookie cutter to cut the dough into shapes. Using a thin spatula, transfer the cookies to the prepared baking sheet, spacing them about 2 inches apart. Refrigerate the scraps.

Step 7

Bake until the tops are dry and the edges begin to turn golden, 10 to 12 minutes. Let cool for about 10 minutes on the pan, then move the cookies to a cooling rack to cool completely. Repeat with the remaining dough and the scraps, re-rolling only once for smooth cookies.

Step 8

Mix a batch of easy cookie icing (choose the thicker border icing). It should fall off the whisk in a thick stream and the fallen ribbon of icing should hold its shape for about 10 seconds before sinking back into the bowl of icing. Remove 2 tablespoons of icing each to 2 small bowls. Stir in 1 or 2 drops of red food coloring into one bowl and 1 or 2 drops of green food coloring into the other bowl until the desired colors are reached. Spoon the colorful icing into two separate zip-top bags or piping bags. Use a pair of scissors to snip ⅛ inch off the tip of each bag.

Step 9

Add additional 1 tablespoon of water, 1 teaspoon at a time, to the remaining white icing until it is at a flooding consistency; the icing falls off the whisk in a fluid stream and the fallen ribbon of icing holds its shape for only a few seconds before sinking back into the bowl of icing. Divide the thinned white icing between two 9-inch baking pans, spreading the icing into an even layer. Drizzle the red icing all over one pan of icing and drizzle the green icing over the second pan. One at a time, put the cookies face-side down in the icing. Take the cookies out one at a time, twisting and shaking gently to let any extra icing drip off, and return to the cooling rack.

Step 10

Allow the cookies to dry completely, 8 hours or overnight. Store the cookies in an airtight container at room temperature for up to 1 week.