Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper.

In a mixing bowl, whisk together the flour, baking powder, baking soda, nutmeg, cinnamon, and salt. Set aside.

In another bowl, cream the softened butter, granulated sugar, and brown sugar together using an electric mixer until light and fluffy (about 3-4 minutes).

Add the eggs one at a time, mixing well after each addition. Then add vanilla extract and rum extract (if using) and mix until combined.

Gradually add the dry mixture to the wet mixture, mixing until just combined. Do not overmix.

Stir in the eggnog until fully incorporated.

Scoop tablespoon-sized portions of dough onto the prepared baking sheet, leaving about 2 inches between each cookie.

Bake in the preheated oven for 10-12 minutes, or until the edges are lightly golden. The centers may appear soft but will firm as they cool.

Allow cookies to cool on the baking sheet for 5 minutes, then transfer them to a cooling rack to cool completely.

For frosting (if using), whisk together powdered sugar, eggnog, and a pinch of nutmeg until smooth. Drizzle or spread onto cooled cookies.