Make the doughnuts: In a small saucepan, combine the cider with the cloves, orange peels, cinnamon sticks and allspice berries. Bring to a boil and cook until reduced to ⅓ cup, 25 to 30 minutes. Strain into a bowl and set aside.
Meanwhile, make the cinnamon sugar: In a medium bowl, mix together the sugar and cinnamon until incorporated.
Make the apple cider caramel: In a medium saucepan, heat the sugar and apple cider over medium-high heat. Cook until the sugar has dissolved and reduced to a dark-amber syrup, 12 to 14 minutes. Whisk in the remaining ingredients to form a smooth caramel, then remove from the heat and let cool slightly.
In a large bowl, mix together the flour, baking powder, cinnamon, salt, nutmeg and baking soda.
To the reduced syrup, whisk in the buttermilk, apple butter, apple cider vinegar and vanilla extract.
In the bowl of a stand mixer fitted with the paddle attachment, cream the butter with the granulated and brown sugars until light and fluffy. With the motor running, add the eggs, 1 at a time, and beat until incorporated. Add the dry ingredients and mix until a dry dough comes together, then stream in the cider mixture until a smooth dough forms.
In a heavy-bottomed pot, such as a 6-quart Dutch oven, heat 2 inches of vegetable oil to 350º. On a lightly floured surface, roll the dough into an 11-by-15-inch rectangle, ½ inch thick. Using a 3½-inch round cutter, cut out 8 rounds. Using a 1¼-inch cutter, cut out the center of each round to make 8 doughnuts and 8 doughnut holes. Reroll the scraps to form 4 more doughnuts and 4 more doughnut holes.
Working in batches, fry the doughnuts and doughnut holes, flipping once, until puffed and golden brown, 2 to 3 minutes per side for the doughnuts and 1 minute per side for the holes. Transfer to a baking sheet lined with a wire rack to drain for a few seconds, then using tongs, toss them in the cinnamon sugar to coat.
Transfer the doughnuts and doughnut holes to a platter and serve immediately with the warm caramel on the side.