Preheat the oven to 350° F. Spray donut molds with nonstick spray and set aside.
In a large bowl, whisk together the flour, baking powder, baking soda, salt, pumpkin pie spice, and brown sugar.
1 cup all-purpose flour, 1 tsp baking powder, ¼ tsp baking soda, ½ tsp salt, 1 tsp pumpkin pie spice, ⅓ cup brown sugar
In a large measuring cup or medium bowl, whisk together the pumpkin puree, melted butter, egg, milk, and vanilla. Pour this mixture into the dry ingredients, and mix until just combined.
½ cup pumpkin puree, 2 tbsp unsalted butter, 1 large egg, ¼ cup milk, 1½ tsp vanilla extract
Scoop this mixture into a piping/ziploc bag to pipe into the donut pan. You could also just spoon the batter into the pan if you prefer. Fill the donut pan ½ full with batter. Don't overfill the donuts because they rise while baking. If you are using silicone donut molds, place them on a baking sheet before putting them into the oven.
Bake for 9-12 minutes until golden brown on top. Transfer the donut pan to a wire rack and allow the donuts to cool for about 5 minutes. Carefully take the donuts out of the pan and allow them to cool for 10-15 minutes before coating them with sugar.
In a shallow bowl, mix the sugar and pumpkin pie spice. Brush the top, bottom, and sides of the donuts with a little bit of melted butter, and then coat with the sugar mixture. Shake off any excess and repeat for the rest.
½ cup granulated sugar, ½ tsp pumpkin pie spice, 1-2 tbsp unsalted butter