Preheat the oven to 325 degrees F and place an oven rack in the center position. Grease a 9x5-inch loaf pan and line the bottom with parchment paper.
Whisk the flour, nutmeg, cinnamon, and salt together and set aside.
In a stand mixer with the paddle attachment, cream the butter and sugar together on high speed until light and fluffy, approximately 5 minutes. Scrape down the sides of the bowl and mix on high speed for another 30 seconds. Turn the mixer speed down to medium-low and add the room temperature eggs, one at a time, allowing them to incorporate completely before adding the next. Scrape down the sides of the bowl, add the vanilla and eggnog and then mix again until everything is just combined.
On low speed, add the dry ingredients in 3 batches and mix until the batter is just combined.
Pour the batter into the reserved loaf pan and smooth the top with a spatula.
Bake for 70-75 minutes, or until a toothpick inserted into the center comes out clean. Allow the cake to cool for 5 minutes in the pan and then gently flip onto a cooling rack. Allow the cake to cool to room temperature.
While the cake is cooling, prepare the glaze: Whisk together dark rum, eggnog, and confectioners’ sugar until smooth.