Preheat the oven to 325°F. Grease and flour a 12-cup bundt pan (or spray with Baker's Joy spray), ensuring all of the crevices are coated.
Add butter and sugar to the bowl of a stand mixer fitted with the paddle attachment (or a large mixing bowl if using an electric hand mixer). Beat together until very light and fluffy, about 4-5 minutes.
Add the eggs one at a time, mixing well after each addition.
Add in the vanilla extract and rum extract (if using). Mix well to incorporate.
In a separate mixing bowl, whisk together the flour, baking powder, salt, and nutmeg.
With the mixer on low speed, alternate adding the flour mixture and eggnog to the butter mixture, beginning and ending with the flour mixture. Mix just until combined.
Spread the batter evenly into the prepared bundt pan. Bake for 65–75 minutes, or until a toothpick inserted into the center of the cake comes out clean (or with just a few moist crumbs).
Remove from oven and let the cake cool in the pan for about 15 minutes.
Run a knife along the edges of the cake to ensure it's loosened from the pan, then invert the cake onto a wire rack or serving plate to cool completely.
Prepare the glaze by whisking together the powdered sugar, eggnog, vanilla extract, and nutmeg until smooth. If the glaze is too thin, add a little more powdered sugar. If it's too thick, add a little more eggnog. You can tit to be thin enough to drizzle, but not so thin that it will run right off the cake.
Drizzle the glaze over the cooled cake, then let the glaze set for about 15 minutes.
Serve and enjoy!