01 - Preheat the oven to 350°F. Lightly grease a 12-cavity donut pan.
02 - In a small saucepan over medium heat, simmer the apple cider until reduced by half to 1/2 cup (about 10–15 minutes). Set aside to cool.
03 - Whisk together the flour, sugar, baking powder, baking soda, cinnamon, nutmeg, and salt in a large bowl.
04 - In a separate bowl, whisk the reduced apple cider, melted butter, milk, eggs, and vanilla extract until well combined.
05 - Add the wet ingredients to the dry ingredients and gently mix until just combined, avoiding overmixing.
06 - Spoon or pipe the batter evenly into the prepared donut pan, filling each cavity approximately three-quarters full.
07 - Bake for 10 to 12 minutes or until the donuts spring back lightly when touched.
08 - Allow donuts to cool in the pan for 5 minutes, then transfer them to a wire rack to cool completely.
09 - Mix the sugar and cinnamon in a shallow bowl. Brush the warm donuts with melted butter and then toss them in the cinnamon sugar mixture until coated.
10 - Serve the donuts warm or at room temperature for best flavor.