01 - In a small saucepan, simmer 1 cup of apple cider over medium heat until it reduces to approximately 1/3 cup. This process should take about 10–12 minutes. Set aside to cool.
02 - In a medium mixing bowl, whisk together the all-purpose flour, baking powder, baking soda, salt, ground cinnamon, and ground nutmeg.
03 - In a large mixing bowl, cream the softened unsalted butter with the granulated sugar and packed brown sugar until the mixture becomes light and fluffy.
04 - Beat in the large eggs one at a time. Then, mix in the reduced apple cider, whole milk, and vanilla extract until thoroughly combined.
05 - Gradually add the dry ingredients to the wet ingredients, stirring until just combined. Avoid overmixing the batter.
06 - Cover the bowl and refrigerate the dough for at least 1 hour, or up to overnight, to make it easier to handle.
07 - Preheat your oven to 375°F (190°C). Lightly grease a doughnut pan.
08 - Spoon or pipe the doughnut batter into the prepared doughnut pan, filling each cavity about two-thirds full.
09 - Bake for 12–15 minutes, or until the doughnuts spring back when gently touched and a toothpick inserted into the center comes out clean.
10 - While the doughnuts are baking, combine the 1/2 cup of granulated sugar and 2 teaspoons of ground cinnamon in a shallow bowl for the coating.
11 - Allow the doughnuts to cool in the pan for 5 minutes before carefully transferring them to a wire rack.
12 - Brush the warm doughnuts with melted unsalted butter, then immediately roll them in the cinnamon sugar mixture to coat evenly.