Preheat the oven to 350 degrees F and grease a donut pan. Whisk the flour, baking powder, baking soda, pumpkin pie spice, cinnamon, and salt together in a large bowl.
In a separate bowl, whisk the pumpkin puree, brown sugar, granulated sugar, oil, eggs, milk, and vanilla until smooth.
Fold the wet ingredients into the dry until just combined. Do not overmix.
Scoop the batter into a large zip-top bag, snip off one corner, and pipe it into the donut pan, filling each well about three-quarters full.
Bake for 12 to 14 minutes, until the donuts spring back when lightly touched. Let cool in the pan for a couple of minutes, then turn out.
Coat the Donuts
Stir the granulated sugar and cinnamon together in a shallow bowl.
Brush each warm donut with melted butter, then roll it in the cinnamon sugar until fully coated. Serve warm.
Notes
Do not overmix. Stir just until the flour disappears for tender donuts.
Fill three-quarters full. This keeps the ring shape and center hole.
Coat while warm. Warm donuts hold the cinnamon sugar best.
No donut pan? Bake in a muffin tin for donut muffins, adding a few extra minutes.