Reduce the cider: Simmer 1 1/2 cups apple cider in a small saucepan over medium heat until reduced to 1/2 cup (about 15-20 minutes). Let cool.
Preheat oven to 350°F (175°C) and grease your doughnut pan.
Mix dry ingredients: In a large bowl, whisk flour, baking powder, baking soda, cinnamon, nutmeg, and salt.
Mix wet ingredients: In another bowl, whisk melted butter, brown sugar, granulated sugar, eggs, milk, vanilla, and cooled cider reduction.
Combine: Add wet to dry and stir just until combined — don’t overmix.
Fill pan: Spoon batter into a zip-top bag, snip the corner, and pipe into the greased doughnut pan.
Bake: 10–12 minutes until springy to the touch.
Cool briefly: Let sit 5 minutes, then transfer to a wire rack.
Coat: While still warm, brush with melted butter and toss in cinnamon sugar.