Preheat oven to 375°F. Butter two doughnut pans and set aside.
In large mixing bowl, whisk or sift together flour, sugar, baking powder, cinnamon, nutmeg and salt. In separate bowl, whisk together the eggnog, eggs, butter and rum, if using.
Make well in center of dry ingredients and pour in wet ingredients. Fold together using rubber spatula until it comes together. Do not over mix.
Spoon batter evenly into prepared doughnut pans and bake until lightly golden brown and toothpick inserted in middle comes out clean, about 8 to 10 minutes.
Remove from oven and let cool slightly. Turn doughnuts out onto wire rack and let cool completely before glazing.
Meanwhile, make the glaze. In medium bowl, whisk together powdered sugar, cinnamon, salt, vanilla, eggnog and as much milk as needed to create a smooth glaze. It should be thick enough to dunk doughnuts in without dripping too much. If it’s too thick, add a splash of milk. If it’s too thin, stir in more powdered sugar.
Dunk cooled doughnuts upside down into glaze and then garnish with sprinkles, if desired. Let set for about 5 minutes before eating. Leftovers can be stored wrapped tightly at room temperature for up to 3 days.