Step 1: Preheat your oven to 350°F (175°C) and generously grease two 6-cavity donut pans with non-stick spray or butter.
Step 2: In a medium bowl, whisk together the flour, baking powder, 1.5 teaspoons cinnamon, nutmeg, and salt until well combined.
Step 3: In a separate large bowl, beat the egg with the granulated sugar and brown sugar until smooth and pale.
Step 4: Stir in the applesauce, reduced apple cider, milk, melted butter, and vanilla extract until the wet mixture is uniform.
Step 5: Gradually add the dry ingredients to the wet ingredients, stirring with a spatula just until no streaks of flour remain. Do not overmix.
Step 6: Transfer the batter to a piping bag and fill each donut cavity about 3/4 full.
Step 7: Bake for 12-15 minutes, or until a toothpick inserted comes out clean and the tops spring back when lightly touched.
Step 8: Allow the donuts to cool in the pan for 5 minutes before transferring them to a wire rack.
Step 9: While donuts are warm, dip each side into melted butter and then toss in the cinnamon-sugar mixture to coat thoroughly.