In a large mixing bowl, whisk together the all-purpose flour, granulated sugar, baking powder, pumpkin pie spice, and salt. Ensure there are no large lumps and that the spices are evenly distributed throughout the flour mixture.
In a separate medium bowl, whisk together the pumpkin puree, egg, milk, melted butter, and vanilla extract until the mixture is smooth and well combined.
Gently fold the wet ingredients into the dry ingredients using a spatula. Mix just until the flour disappears. Be careful not to overmix, as this can make the donuts tough instead of fluffy.
Lightly grease a silicone donut pan that fits inside your air fryer, or pipe the batter into circles on a piece of parchment paper cut to fit the basket. You can also use a spoon to fill the molds about 3/4 full.
Place the donuts in the air fryer basket. Cook at 350°F (175°C) for 7 to 9 minutes, or until a toothpick inserted into the center comes out clean. If you are not using a mold, ensure the donuts are not touching each other to allow for proper airflow.
While the donuts are cooking, melt the 1/4 cup of butter in a small bowl. In another small bowl, mix together the granulated sugar and ground cinnamon for the topping.
Once the donuts are done, remove them from the air fryer and let them cool for just a minute so you can handle them. Brush each donut with melted butter and then toss it in the cinnamon-sugar mixture until fully coated.