Preheat the oven to 350℉. Grease doughnut tins well with non-stick cooking spray or butter.

Whisk together the melted butter, sugar, and brown sugar in a large mixing bowl. Add the eggs, vanilla, sour cream, and eggnog and whisk until combined.

In another bowl, whisk together the flour, baking powder, baking soda, and nutmeg until combined. Add to the wet ingredients and stir just until incorporated. Do not overmix!

Transfer the batter to a Ziploc bag with the corner snipped off or a piping bag fitted with a wide tip. Pipe the batter into the prepared doughnut tin(s), filling each doughnut well about ½ full.

Bake in the preheated oven for 10-12 minutes or until a toothpick inserted into the center of the doughnut comes out clean. Let cool in the pans for 5 minutes before transferring to a wire rack to finish cooling completely before glazing. Bake the remaining doughnuts.

Whisk together the eggnog and powdered sugar in a bowl until a nice icing consistency is reached, adding more powdered sugar or eggnog as needed. Dip the cooled doughnuts in the icing or drizzle the icing on top.