In a large bowl, whisk together the flour, sugar, baking powder, salt and pumpkin pie spice. In a smaller bowl, whisk together the egg, milk, pumpkin cider, pumpkin puree and butter. Add the wet ingredients to the dry and stir together until just combined.
Heat a large saucepan over medium heat and fill it with about 3 inches of oil. Fit the pot with a candy thermometer - you want the oil to be about 375 degrees F to fry.
You can either take the dough and scoop it into the oil once hot, or you can lightly flour you hands and roll the dough into 1-inch balls so the holes are smoother. I did the latter.
Once the oil has reached 375 degrees F, add the dough balls 2 or 3 pieces at a time and fry until golden brown (keep an eye on the oil temp!), turning over a few times, for 2 to 3 minutes total. Remove the doughnut holes and place them on a paper towel to drain any excess grease.
Once the doughnuts are finished, roll them in the mixture of the sugar and pumpkin pie spice. Serve with the hot fudge!