Preheat the oven to 375°F and grease a standard 12-cup muffin pan well or line with paper liners.

Add the apple cider to a small saucepan and simmer over medium heat until reduced to 1/2 cup, about 10 to 15 minutes. Set aside to cool slightly.

In a medium bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, and nutmeg.

In a large bowl, whisk the melted butter, brown sugar, and granulated sugar until smooth. Add the eggs and vanilla and whisk until glossy and combined.

Whisk the reduced cider and milk into the wet mixture.

Add the dry ingredients to the wet ingredients and stir gently just until no dry streaks remain.

Divide the batter evenly among the muffin cups, filling each about three-quarters full.

Bake for 16 to 18 minutes, until lightly golden and a toothpick inserted in the center comes out clean.

Cool the muffins in the pan for 5 minutes, then transfer to a rack.

In a small bowl, stir together the granulated sugar and cinnamon for the coating.

Brush each warm muffin all over with melted butter, then roll in the cinnamon sugar until fully coated.

Serve warm or at room temperature.