Step 1: Reduce the Apple Cider. In a small saucepan, bring 2 cups of apple cider to a boil over medium-high heat. Reduce the heat to medium-low and simmer gently until the cider has reduced to about 1/2 cup (this will take 15-20 minutes). Set aside to cool completely.
Step 2: Prepare Your Equipment. Preheat your oven to 350°F (175°C). Grease and flour two standard 6-cavity donut pans.
Step 3: Combine Dry Ingredients. In a large bowl, whisk together the all-purpose flour, 1/2 cup granulated sugar, baking powder, baking soda, salt, 1 teaspoon ground cinnamon, and freshly grated nutmeg.
Step 4: Combine Wet Ingredients. In a separate medium bowl, whisk together the 1/4 cup melted unsalted butter, milk, large egg, and the cooled, reduced apple cider.
Step 5: Combine Wet and Dry. Pour the wet ingredients into the dry ingredients. Stir gently with a spatula until just combined. Be careful not to overmix.
Step 6: Fill Donut Pans. Transfer the batter to a large zip-top bag or a piping bag. Snip off a corner of the bag and pipe the batter evenly into the prepared donut cavities, filling each about two-thirds full.
Step 7: Bake. Bake for 12-15 minutes, or until the donuts are golden brown and spring back when lightly touched. Let them cool in the pans for 5 minutes before carefully transferring them to a wire rack to cool further.
Step 8: Prepare Cinnamon Sugar Coating. While the donuts are cooling slightly, melt the remaining 4 tablespoons of unsalted butter in a shallow bowl. In another shallow bowl, combine the remaining 1/2 cup granulated sugar and 1/2 teaspoon ground cinnamon for the coating.
Step 9: Coat the Donuts. Once the donuts are cool enough to handle but still warm, dip each donut into the melted butter, ensuring it’s fully coated. Then, immediately transfer it to the cinnamon sugar mixture and roll to coat completely. Serve warm.