Preheat the oven to 350°F. Line a large cookie sheet with parchment paper and set aside.

In a large bowl of a stand mixer fitted with the paddle attachment or a hand mixer, beat the butter and sugar together on medium-high speed for 2 minutes.

Add the egg, vanilla and rum extract then beat well, until the yellow streaks are gone.

Add the eggnog and beat again until it's incorporated.

Whisk the flour, baking powder, baking soda, salt, and nutmeg in a separate medium bowl. With the mixer on low, add half of the dry ingredients, then turn the speed up to medium to incorporate it fully. Repeat the process with the second half of the dry ingredients. The cookie dough will be wet, this is what you want!

Use a heaping tablespoon or medium cookie scoop to drop the dough a few inches apart on a parchment lined baking sheet. Bake for 10 to 12 minutes or until the tops are set and no longer look wet. The cookies will spread out first then start to rise.

Allow to cool on cookie sheet for a few minutes then transfer to wire rack to cool completely before frosting.

Beat together the softened butter and cream cheese in a large bowl until smooth and all of the lumps are gone.

Add 1 cup of the confectioner's sugar and beat on medium speed to incorporate. Add the eggnog, vanilla and rum extract and beat until combined and the mixture is smooth.

Finish by adding the last 2 cups of confectioners' sugar and beat well until smooth.

Frost the cooled cookies with a tablespoon or two of the frosting. I like to make a swirling motion on the top. Sprinkle with more ground nutmeg before serving.