• First, in a small saucepan, over high heat, bring the apple cider up to a boil. Boil it for about a minute, then reduce the heat to medium-low and simmer until reduced to 1/2 cup; this will take about 15-20 minutes.
  
• The cider will thicken a little bit and it will get slightly deeper in color. After that, let the cider cool completely before using it.
• Preheat the oven to 375 degrees F.
• Grease a donut pan with non-stick cooking spray and set it aside.
• Next, in a large bowl whisk together the flour, baking powder, cinnamon, salt, and nutmeg, and set it aside.
  
• In another bowl, whisk together the 1/2 cup reduced apple cider, milk, brown sugar, white sugar, egg, butter, and vanilla extract.
  
• After that, add the flour mixture to the wet ingredients and stir just until combined.
  
• Transfer the batter to a large zip-top bag. Cut off about 1/2 inch off one of the bottom corners and pipe the batter into the prepared donut pan, so each hole is about 1/2 full.
• Bake for 8-10 minutes until they are cooked through. You can stick a toothpick into the center of the donut, and if it comes out clean, they are done. Place the donuts onto a cooling rack.
  

Topping:

• In a medium mixing bowl, combine the sugar, cinnamon, and nutmeg.
• Brush the donuts on both sides with the melted butter.
  
• Roll them into the cinnamon mixture, so all sides are covered. Repeat this with each donut. Serve and enjoy!