Reduce the cider: Pour the apple cider into a small saucepan and simmer over medium heat until it reduces to about 1/2 cup.
This usually takes 12–15 minutes. Cool to room temperature.
Brown the butter: In a light-colored pan, melt the butter over medium heat. Swirl until it foams, then turns golden with toasty brown bits and a nutty aroma.
Remove from heat and cool slightly. You should have close to 1/2 cup browned butter.
Prep the pan and oven: Heat the oven to 350°F (175°C). Lightly grease a standard donut pan (12 cavities) with baking spray or a thin film of butter.
Mix dry ingredients: In a bowl, whisk flour, baking powder, baking soda, salt, cinnamon, nutmeg, and allspice.
Cream sugars with brown butter: In a larger bowl, combine granulated sugar, brown sugar, and the slightly cooled brown butter.
Whisk until glossy and well combined.
Add eggs and flavorings: Whisk in eggs one at a time, then add vanilla, reduced cider, and sour cream. Mix until smooth.
Combine wet and dry: Add the dry mixture to the wet in two additions. Stir gently with a spatula just until no dry streaks remain. Do not overmix.
Fill the pan: Spoon or pipe the batter into the donut cavities, filling each about 3/4 full.
A zip-top bag with the corner snipped works well for piping.
Bake: Bake 10–12 minutes, until the tops spring back when lightly pressed and a toothpick comes out clean or with a few moist crumbs.
Cool briefly: Let the donuts rest in the pan for 5 minutes, then turn them out onto a rack. They should be warm but not too hot to handle.
Coat in cinnamon sugar: Mix the coating sugar, cinnamon, and pinch of salt in a shallow bowl. For an extra-sandy crust, lightly brush warm donuts with melted butter, then toss in the cinnamon sugar until well coated.
Serve: Enjoy warm.
The aroma alone is worth the effort.