Add 2 ¾ cups all-purpose flour, 1 ¼ teaspoons baking powder, ¼ teaspoon baking soda, ½ teaspoon salt, 1 tablespoon cornstarch, ¼ teaspoon ground cinnamon, and ½ teaspoon ground nutmeg in a mixing bowl. Whisk together and set aside.

In the bowl of a stand mixer or in a mixing bowl with a hand mixer cream ¾ cup butter and 1 ¼ cups granulated sugar together on medium speed until light and fluffy, about 2-3 minutes. Add in the 1 ½ teaspoons vanilla and ½ teaspoon rum extracts and ¾ cup sour cream and mix again until combined, about a minute. Now add the 2 eggs one at a time and mix until just combined.

Add the dry ingredients and mix on low in 2-3 batches until the dough just comes together.

Chill the cookie dough, covered, in the fridge for at least 45 minutes to an hour, and up to 2 days.

Preheat the oven to 375°F / 190°C and line a baking sheet with parchment or a silicone baking mat.

Remove from fridge and let stand at room temperature for a bit if too difficult to scoop. Scoop dough with a 1 ½ tablespoon cookie scoop and roll into a ball. Place on baking sheet a few inches apart and press down center with thumb.

Cook for 8-10 minutes (mine usually takes 9). Remove them from the oven and let them cool on the baking sheet for at least 5 minutes before moving to a cooling rack.

While the cookies are cooling, you can make the eggnog buttercream.

In the cleaned bowl of a stand mixer, or in a large mixing bowl with a hand mixer, cream the ½ cup of unsalted butter and half of the 3 cups of powdered sugar together on medium speed. Once combined, add the rest of the sugar, ¼ teaspoon salt, and ½ teaspoon ground nutmeg and continue mixing until well combined.

Add the ¼ teaspoon vanilla extract, ¾ teaspoon rum extract, and ¼ cup heavy cream and mix on low until combined, then at higher speed until fluffy and spreadable consistency.

Pipe or spread the frosting onto the cooled cookies and add sprinkles if desired.