Pre-heat oven to 325 degrees and lightly spray a doughnut pan with oil.
Whisk together flour, sugar, baking powder, cinnamon, nutmeg, and salt in a large bowl.
In a separate small bowl, whisk eggs. Then add in and whisk together eggnog, rum, and melted butter, until combined.
Stir the wet ingredients into the dry ingredients until combined, being very careful not to over-mix (that’s what causes the dense cake-y doughnuts).
Fill doughnut pan about 3/4 of the way with batter. I like to put batter in a Ziplock bag (or pastry bag), cut the corner off, and squeeze batter into doughnut pan.
Bake for 10-12 minutes until doughnuts are cooked through and springy to the touch. Let doughnuts cool in pan for a couple minutes before moving to wire racks to cool completely. Repeat with remaining batter, making sure to spray doughnut pan with oil again.
Once cooled, dip doughnuts in icing (I like to double dip) and top with sprinkles, if desired.