Preheat oven to 350 degrees F. Line two baking sheets with parchment paper.
Beat the butter, granulated sugar, and brown sugar together in a large bowl for 2-3 minutes until creamy and light.
3/4 cup salted butter, 1/2 cup granulated sugar, 1/2 cup packed light brown sugar
Add the egg yolks, vanilla, and rum extracts, then beat again. Stop and scrape the bottom and sides of the bowl then add the eggnog and mix again.
2 egg yolks, 1 teaspoon vanilla extract, 1/2 teaspoon rum extract, 1/2 cup eggnog
Add the flour, baking powder, salt, nutmeg, and cinnamon, then mix until combined, scraping the bottom and sides of the bowl again.
2 1/2 cups all-purpose flour, 2 teaspoons baking powder, 1/2 teaspoon salt, 1/2 teaspoon ground nutmeg, 1/4 teaspoon ground cinnamon
Use a small cookie scoop to scoop the dough onto the prepared baking sheets, spacing them a couple inches apart. Bake for 10-12 minutes until set so they stay nice and soft, but they shouldn't brown much around the edges. Cool completely.