In a large bowl, whisk together egg, yolk, pumpkin, and buttermilk until combined. Add sugars and butter and continue whisking. Stir in baking powder, pumpkin pie spice, salt, and baking soda.
Carefully fold in flour until a sticky dough forms. Cover the bowl and place it in the freezer for 15 minutes.
Pat or roll out dough on a well-floured surface to about ½" thick. Cut with a donut cutter (or use a 3" and 1" biscuit or round cutter that's been dipped in flour. Transfer the donuts and holes to a baking sheet lined with parchment paper that's been dusted with flour.
If deep frying or shallow frying, heat oil to 370° F. Fry donuts in batches until browned, about 3 minutes, turning once. The donut holes will fry much faster than the larger donuts. Drain on paper towels.
If air frying, spray donuts with nonstick spray and place in a single layer in air fryer that's been preheated to 370° F. "Fry" for about 5-6 minutes, depending on the wattage of your air fryer.
Mix cinnamon and sugar together in a brown paper bag or plastic ziptop baggie. Drop warm donuts into bag and shake.
Apple Cider Glaze
Heat the apple cider and the salt in a small saucepan over low heat until hot. Remove from heat and add the powdered sugar, whisking to combine.