Preheat your oven to 325°F (163°C). Generously grease and flour a bundt pan, ensuring all crevices are well-coated to prevent sticking.
In a medium-sized bowl, whisk together the cake flour, baking powder, salt, cinnamon, and nutmeg. Set this dry mixture aside for later use.
In the bowl of an electric mixer fitted with a paddle attachment (or using a hand mixer), beat the softened butter on medium speed until it becomes smooth and creamy. Gradually add the white sugar and light brown sugar, mixing until the mixture is light in color and fluffy, about 3 to 5 minutes.
Add the eggs one at a time, beating well after each addition to ensure the yolk is fully incorporated before adding the next.
Stir the vanilla extract into the eggnog and set it aside.
With the mixer on low speed, add the flour mixture alternately with the eggnog mixture, beginning and ending with the dry ingredients. Add the flour mixture in three parts and the eggnog mixture in two parts. Mix just until everything is combined; avoid overmixing to keep the batter light.
Pour the batter evenly into the prepared bundt pan and smooth the top with a spatula. Bake in the preheated oven for about 1 hour, or until a toothpick inserted into the center of the cake comes out clean or with only a few moist crumbs attached. Check the cake around the 50-minute mark to avoid overbaking. If the top is browning too quickly, cover it loosely with aluminum foil.
Once baked, allow the cake to cool in the pan for about 10 minutes before inverting it onto a serving plate. Let the cake cool completely before applying the glaze.