1-Preheat the oven to 350°F (180°C). In a mixing bowl, whisk together 2 cups of all-purpose flour, 2 teaspoons of baking powder, 1/2 teaspoon of salt, 1/2 teaspoon of ground nutmeg, and 1/2 teaspoon of ground cinnamon for 30 seconds, then set aside.

2-In the bowl of an electric stand mixer fitted with the paddle attachment, whip together 3/4 cup of unsalted butter, 1/2 cup of granulated sugar, and 1/2 cup of packed light brown sugar until pale and fluffy.

3-Mix in 2 large egg yolks one at a time, blending just until combined after each addition. Add 1 teaspoon of vanilla extract, 1/2 teaspoon of rum extract, and 1/2 cup of full-fat eggnog, mixing to incorporate.

4-With the mixer on low speed, slowly add the dry ingredients and mix just until combined.

5-Scoop heaping tablespoonfuls of dough onto baking sheets lined with parchment paper or a silicone mat, spacing the cookies 2 inches apart.

6-Bake for 11 to 13 minutes. Let the cookies rest on the baking sheet for a few minutes before transferring to a wire rack to cool completely.

7-For the frosting, whip 1/4 cup of unsalted butter and 1/4 cup of salted butter together until very pale and fluffy. Add 1/2 teaspoon of rum extract and 3 tablespoons of eggnog, then gradually mix in 3 cups of powdered sugar. Add 1 to 2 more tablespoons of eggnog as needed to reach the desired consistency.

8-Spread the frosting over the cooled cookies and lightly sprinkle with additional ground nutmeg.