Preheat the oven to 350°F. Spray a 9x13 baking dish with baking spray, set aside. In a medium-sized bowl, mix together the flour, baking powder, salt, nutmeg, and baking soda, set aside.
In the body of a stand mixer with the paddle attachment, cream the butter with the sugar for 3 minutes until light and fluffy, scrape down the sides as needed.
Add the eggs into the mixer one at a time, mixing them in fully before adding the next one.
Add the vanilla and rum extract until smooth, the mixture may look a little curdled, that’s okay.
Add half of the flour mixture and mix in until combined.
Mix in the sour cream until combined. Repeat with the remaining flour.
Slowly stir in the eggnog, scrape down the sides and give another mix so everything is smooth.
Pour the batter into the baking dish and smooth out the top. Bake for 35-42 minutes until a toothpick inserted into the center comes out clean. Place on a wire rack to cool completely.
While the cake is cooling, start the frosting. Place the eggnog and flour into a small saucepan and whisk to combine. Place over medium heat, stirring constantly until the mixture is thick like a paste. Let cool to room temperature.
Place the butter and powdered sugar in the body of a stand mixer with the paddle attachment. Slowly stir it in until combined. Add the vanilla and nutmeg, stir to combine. Add the cooled eggnog/flour mixture, stir it in until combined, then turn the mixer on medium-high speed. Whip it for 3 minutes until light and fluffy with a whipped cream texture.
Frost the cake and add Christmas sprinkles if using or a sprinkle of ground nutmeg would also be pretty. Slice and serve.