Preheat your oven to 425 degrees F and lightly grease a doughnut pan (I used a touch of butter).
In a bowl, whisk together the flour, sugar, baking powder, cinnamon, nutmeg and salt.
In another bowl, whisk together the 1/2 cup eggnog, egg, coconut oil and vanilla.
Mix the wet ingredients into the dry ingredients just until combined. Don't over mix or you'll get chewy donuts.
Spoon the batter into the donut pan, filling each round about 3/4 full.
Bake the donuts for 7 minutes and then place them on a cooling rack or even just a paper towel and give them a little time to cool down before you put on the glaze.
To make the glaze: whisk the vanilla and then the eggnog one Tablespoon at a time into the powdered sugar. You want it to have a fairly thin consistency, but enough substance that it's not all going to run off the donut.
Once the donuts have cooled, you can used a spoon to drizzle the glaze over the donuts or a spatula to lightly spread it across the top of each donut.
Sprinkle with holiday colored sprinkles to make them a bit more festive or you can simply grate a small amount of extra nutmeg over them.