Preheat oven to 350 F and grease and flour a 12 cup bundt pan.
In the bowl of a stand mixer fitted with the paddle attachment, combine eggs and sugar. Beat at medium-high speed for 4–6 minutes, until pale and fluffy (see picture above for reference).
With the mixer running on low speed, add the vanilla extract, vegetable oil and the eggnog in a slow stream. Add the rum and mix until combined.
Combine flour, baking powder, and salt. Sieve into the stand mixer bowl and mix at low speed until just combined. Pour into prepared baking pan.
Bake for 45-55, until a skewer, inserted in the center, comes out clean with only a few moist crumbs attached.
Let the cake cool for 15 minutes in the pan on a cooling rack, then turn out the cake onto the cooling rack and let cool completely.
Combine all the ingredients for the glaze and pour it over the cake. Instead of a glaze, you can also sprinkle the cake with powdered sugar.