This is the perfect doughnut to celebrate fall. Scented with warm spices, flavored with cider and studded with tart apples, these doughnuts are best served the same day they are made.

In a small saucepan add apple cider and bring to a boil over medium-high heat. Reduce cider down to ½ cup, about 20 minutes. Set aside to cool.

Sift together the flour, baking powder, baking soda, salt and spices into a medium bowl and set aside.

In a bowl of a stand mixer fitted with a paddle attachment, cream together the butter with both the sugars until light and fluffy. Scrape the sides and bottom of the bowl occasionally with a silicone spatula. Add eggs, one at a time, mixing until each addition is incorporated. Add the reduced cider, buttermilk and vanilla and mix until well combined. Add the flour mixture and mix until well incorporated. Fold in apples and stir until combined.

Lightly dust a work surface with flour, turn the dough out and roll into a 12-inch by ½-inch thick round. Using floured 3½-inch and 1½-inch ring cutters, cut out the doughnuts and holes; gather and reuse the dough scraps. Pour the oil to 4 inches deep in a large heavy-saucepan or a deep fryer with deep-fry thermometer attached and heat to 325°F.

Working in batches, carefully place the doughnuts in the oil, cook, flipping once, until puffed and golden, about 3 to 4 minutes. Using a slotted spoon, transfer to wire rack placed over a baking sheet.

In a large bowl combine the sugar with the cinnamon and mix until thoroughly combined. Toss warm doughnuts in the cinnamon sugar and shake off excess.