Preheat the oven to 350°F (180°C). Brush the donut pan with a little oil.
In a medium bowl, combine the flour, sugar, baking soda, baking soda, cinnamon, nutmeg, and salt. Whisk in the remaining ingredients just until combined.
Using a large round tip on a large decorating bag. Fill the bag with dough and pipe around each well until it’s about ¾ full. Bake for 8–10 minutes, or until the donuts spring back when lightly pressed.
Remove from the oven to a cooling rack. Let the donuts cool in the pan for 5 minutes.
Cool on the racks completely before frosting. If using cinnamon sugar, toss in while still warm.
Glaze: Whisk together all of the ingredients in a small bowl. Place a sheet of parchment paper under the cooling rack. Let the donuts stand until the glaze sets. Place the glaze in a medium bowl. Dip one donut at a time, top-side down, into the glaze. Swirl and remove, then place glaze-side up on a cooling rack.
While the glaze is still wet, sprinkle with sweetened flaked coconut, chopped nuts, or sprinkles.