Generously grease a 12-cup bundt pan with the shortening then add 1/4 cup of flour to the pan and cover with plastic wrap. Turn and shake the pan to coat the inside with flour. Discard any excess flour.
In a large bowl or stand mixer fitted with a paddle attachment, cream together the softened butter and sugar until pale and fluffy, about 3 minutes.
Scrape down the sides of the bowl and beat in the eggs one at a time, mixing after each addition just until the yolk is no longer visible.
On low speed (stir on a stand mixer), add the remaining flour 1 cup at a time, alternating with the eggnog, beginning and ending with the flour. Add in the vanilla or rum extract and mix until silky smooth.
Transfer the batter into the prepared bundt pan and smooth out the top.
Bake for 75 to 90 minutes at 325°F (DO NOT PREHEAT OVEN) or until a cake tester or toothpick comes clean from the center.
Remove from the oven and allow to cool in the pan for 30 minutes before flipping out onto a cake stand, wire rack, or plate and allowing to cool completely. You can use a small rubber spatula to help loosen the sides, if needed.
In a medium bowl, whisk together the powdered sugar and eggnog for the icing until smooth.
Spread the icing over the top of the cake and then dust with ground nutmeg. Serve at room temperature.