Preheat oven to 375°F. Spray a donut pan with nonstick baking spray and set aside.
In a large bowl using a hand mixer or stand mixer, combine butter, granulated sugar and brown sugar and beat on medium-high speed until combined and creamy.
1/2 cup unsalted butter, 1/3 cup granulated sugar, 1/3 cup light brown sugar
Add egg, yogurt, vanilla and rum and beat again to combine.
1 large egg, 1/2 cup greek yogurt or sour cream, 1 teaspoon Nielsen-Massey Madagascar Bourbon Pure Vanilla Extract, 1 teaspoon rum
In a separate medium bowl, whisk to combine flour, baking powder, baking soda, nutmeg, cinnamon and salt.
Add the flour mixture to the bowl of butter mixture and beat to combine - the batter will look like large crumbs.
Add eggnog and beat on low speed to combine completely.
1/2 cup eggnog
Place a pastry bag in a pint glass with the edges pulled down over the side. Now use a spatula to spoon the batter into the bag. Twist the top of the bag to keep it closed, then cut off the bottom tip - you want the hole to be large enough to pipe into your donut pan.
Pipe batter into prepared donut pan, filling each cavity about 3/4 full. Bake for 8-10 minutes, or until the top edges start to turn golden brown.
Let cool in pan for a few minutes, then transfer to a wire rack to cool completely.
Eggnog Glaze
In a medium bowl, whisk to combine powdered sugar, eggnog, rum, cinnamon and nutmeg.
1 1/2 cups confectioners’ sugar (powdered sugar), 2-3 tablespoons eggnog, 1 teaspoon rum, Pinch of ground cinnamon, Pinch of ground nutmeg, Pinch salt
Add a pinch of salt if it's too sweet for your liking, additional eggnog if it's not thin enough, or additional powdered sugar if it's too thin.
Immediately spread on the tops of cooled donuts, and add sprinkles - the glaze will set quickly!
Assorted festive sprinkles
Serve immediately or store in an airtight container until ready to serve. Enjoy!