Preheat oven to 350 degrees
Combine flour, baking powder, salt, cinnamon and nutmeg in a bowl and mix
In a stand mixer or a handheld mixer mix the butter and sugar until well incorporated
Add in eggs one at a time and mix, then add the vanilla extract and mix
Add a little of dry ingredients, then a little of the apple cider, go back and forth adding the dry ingredients then the wet ingredients until all of both are in the mixer, mixing in between each addition of ingredients. Start with dry ingredients and end with dry ingredients.
Spray donut molds with cooking spray, or grease with butter and pipe in the batter 3/4 of the way to the top using a pastry bag or a gallon bag
Bake 10-13 minutes until cooked through. Test doneness with a toothpick. It should come out clean.
Let wait for one minute and then unmold and put on a wire rack to cool
To make the icing put the cider in a pot and cook until reduced by half, let cool to room temperature. Make sure to mix often so it doesn't stick to the bottom of the pot
Sift the powdered sugar if possible. Then whisk powdered sugar, cinnamon and reduced cider in a bowl.
Put parchment paper underneath the wire rack. Then dip the donuts in the icing, and put back on the wire rack to dry.
Allow 20 minutes for the icing to dry. Then they're ready to enjoy