In a saucepan, bring the water, butter, pumpkin, and salt to a boil, mixing to combine.
Turn off the heat and stir in the flour until the dough is very thick.
Working quickly, add the egg and mix vigorously to combine. Move fast to avoid scrambling the egg — if the egg is not mixed in quickly enough, the churros can taste eggy. A sturdy whisk works best; the egg and pumpkin mixture will come together as you mix.
Scoop the batter into a pastry bag fitted with a large star or round tip. If you do not have a pastry bag or tips, use a zip-top bag and snip off one bottom corner.
Preheat the air fryer for 5 to 10 minutes at 375°F.
Pipe the churro batter into any size or shape you prefer in the air fryer basket. Lightly spray the basket with oil before piping, or line it with parchment.
Air fry for about 15 to 20 minutes. Cooking time may vary with the size and shape of your churros, so watch the first batch closely to be sure they cook through without overcooking.
While the churros cook, stir together the granulated sugar and spices in a bowl or on a plate.
As soon as the churros come out and are still hot, toss them in the sugar mixture until well coated. Set aside to cool.
Best served immediately, but they can be stored in an airtight container.