Preheat the oven to 375°F. Line 2 baking sheets with parchment paper or silicone baking mats and set aside.
In a large bowl, whisk together the flour, cake flour, cornstarch, baking powder, baking soda, salt, nutmeg and cinnamon. Set aside.
2 1/2 cups all purpose flour, 1 1/4 cups cake flour, 2 tsp. cornstarch, 2 tsp. baking powder, 1 tsp. baking soda, 1 tsp. salt, 3/4 tsp. ground nutmeg, 3/4 tsp. ground cinnamon
In a stand mixer fitted with the paddle attachment, cream together the butter and sugars for about 3 minutes on medium speed or until light and fluffy.
1 cup unsalted butter, cold, cubed, 1 cup white sugar, 1/4 cup brown sugar (tightly packed), dark or light
Add in the eggs, one at a time, mixing just until the yellow disappears. Add in the rum extract and eggnog. Scrape down the sides of the bowl as needed.
2 large eggs, 1 large egg yolk, 1 tsp. rum extract, 1/2 cup eggnog, full fat
Gradually add in the dry ingredients on medium-low speed and mix just until combined.
Scoop the dough out using a 2 Tbsp. cookie scoop (and roll into balls with lightly floured hands) and place onto prepared baking sheet, spacing them about 2 inches apart.
Bake for 10-12 minutes, or just until the edges are lightly browned. The cookies will look puffy and they'll settle as they cool.
Allow the cookies to cool on the baking sheet for 10 minutes then transfer to a rack to cool.
Meanwhile, make the eggnog cream cheese frosting. Using a hand held mixer or a stand mixer fitted with the paddle attachment, beat the softened cream cheese and butter on medium speed until it's creamy. About 2 minutes. Add in the eggnog, rum extract and a pinch of cinnamon nutmeg, and salt. Then add in the powdered sugar. Beat on low just to get it combined the increase to medium-high speed until fully incorporated. Adjust as needed, adding more powdered sugar is the buttercream is too thin or a touch more eggnog if too thick.
8 oz. cream cheese, full-fat, softened, 4 Tbsp. unsalted butter, room temperature, 2 Tbsp. eggnog, full fat, 1/2 tsp. rum extract, pinch of cinnamon nutmeg and salt, 3 cups powdered sugar
Spread on top of cooled cooking or you can use a piping bag. Garnish with a sprinkle of nutmeg and/or cinnamon and enjoy!