In a small saucepan, bring 2 cups of apple cider to a boil over medium-high heat. Reduce heat to medium and simmer, stirring occasionally, until the cider has reduced to about 1/2 cup. This will take 15-20 minutes. Let it cool slightly. Preheat oven to 350°F (175°C) and grease two 6-cavity donut pans.

In a large mixing bowl, whisk together the flour, 1/2 cup granulated sugar, baking powder, 1 tsp cinnamon, nutmeg, and salt.

In a separate medium mixing bowl, whisk the egg, milk, 1/4 cup melted butter, vanilla extract, and the cooled 1/2 cup reduced apple cider until well combined.

Pour the wet ingredients into the dry ingredients. Mix with a whisk or rubber spatula until just combined. Be careful not to overmix; a few lumps are okay.

Spoon the batter into a piping bag (or a large Ziploc bag with the corner snipped off) or carefully spoon it directly into the prepared donut pans, filling each cavity about two-thirds full.

Bake for 10-12 minutes, or until the donuts are lightly golden and spring back when gently pressed.

Let the donuts cool in the pans for 5 minutes before carefully transferring them to a wire rack to cool completely.

While the donuts are cooling, melt 1/4 cup unsalted butter in a small bowl. In another small bowl, combine 1/2 cup granulated sugar and 1 tbsp cinnamon.

Once the donuts are cool enough to handle, brush each donut generously with melted butter, then immediately dredge or roll them in the cinnamon sugar mixture, ensuring they are fully coated. Alternatively, you can dip the entire donut quickly into the melted butter before rolling in the sugar.

Serve warm or at room temperature.