Reduce the Cider: Pour 1 1/2 cups of apple cider into a small saucepan. Bring to a boil, then reduce heat and simmer until the cider has reduced to about 1/2 cup. This should take 15-20 minutes. Set it aside to cool completely.

Combine Dry Ingredients: In a large bowl, whisk together the flour, granulated sugar, brown sugar, baking powder, baking soda, cinnamon, salt, nutmeg, and allspice.

Combine Wet Ingredients: In a separate medium bowl, whisk the egg, cooled apple cider reduction, melted butter, and buttermilk until well combined.

Mix Batter: Pour the wet ingredients into the dry ingredients. Stir gently with a spatula until just combined. Do not overmix.

Heat Oil & Fry: Heat 2-3 inches of oil in a heavy-bottomed pot to 350°F (175°C). Pipe or drop batter into the oil and fry for 60-90 seconds per side, until golden brown. Drain on a wire rack.

Preheat & Prepare Pan: Preheat oven to 350°F (175°C). Grease a donut pan. Pipe batter into the pan, filling two-thirds full.

Bake: Bake for 10-12 minutes, or until a toothpick comes out clean. Let cool slightly before moving to a wire rack.

Make Topping: In a shallow bowl, whisk together the granulated sugar and cinnamon.

Coat the Donuts: While donuts are still warm, brush them with melted butter and immediately toss in the cinnamon-sugar mixture until fully coated. Serve immediately.