Preheat your oven to 350°F (175°C). Line a cupcake tin with paper liners.
In a medium bowl, whisk together the flour, baking powder, baking soda, salt, nutmeg, and cinnamon. Set aside.
In a large mixing bowl, cream together the softened butter and granulated sugar until light and fluffy.
Beat in the eggs, one at a time, ensuring each is well incorporated. Mix in the vanilla extract.
Gradually add in the dry ingredients, alternating with the eggnog. Start and finish with the dry ingredients, mixing gently until just combined.
Fill each cupcake liner about two-thirds full with batter.
Bake in the preheated oven for 18-20 minutes, or until a toothpick inserted into the center comes out clean.
Allow the cupcakes to cool in the pan for 5 minutes before transferring them to a wire rack to cool completely.
For the frosting, in a medium bowl, beat the powdered sugar, milk, and rum extract until smooth. Adjust the consistency with more milk or powdered sugar as needed.
Once the cupcakes are completely cooled, pipe or spread the frosting onto each cupcake.
Sprinkle a little ground nutmeg on top for decoration.
Notes
For a stronger flavor, you can add more rum extract to the frosting.