Preheat the oven to 350 degrees. Spray a donut pan with non-stick spray, set aside.
In a medium bowl, whisk together flour, baking soda, baking powder, salt, cinnamon, and nutmeg. Set aside
In a medium bowl combine apple cider, buttermilk, and vanilla. Set aside.
In a stand mixer or large bowl blend unsalted butter, white and brown sugar until fluffy. Add in eggs, one at a time. Blend until well mixed.
At the lowest speed on mixer add 1/2 flour mix and 1/2 cider mix. Blend, then remaining flour and cider mix. Fold ingredients to blend.
Use either a large plastic storage bag and place batter into the bag. Cut the corner off and pipe the batter into the donut pan. Or use a piping bag with a circle tip to pipe the batter into the donut pan
Bake for about 15 minutes. A toothpick would be clean after sticking it into the donut. Let donuts cool about 3 minutes on a cooling rack.
While the donuts are baking, melt the butter in a small saute pan. In a small bowl, combine the white sugar, brown sugar, cinnamon, and nutmeg.
While the donuts are warm, brush them with the melted butter and then dip the donuts in the cinnamon sugar. Place them back on the cooling rack. The donuts can be eaten when warm.