Preheat the oven to 350ºF (175ºC) and spray the donut pan with cooking spray.

Mix the wet ingredients: whisk together pumpkin puree, brown sugar, vegetable oil, and milk until smooth.

Combine the dry ingredients: sift together flour, baking powder, pumpkin pie spice, cinnamon, nutmeg, and salt in a large bowl.

Fold the wet ingredients into the dry ingredients until just combined; a few lumps are fine.

Fill the donut pan cavities about ¾ full with the batter using a piping bag.

Bake for 15–16 minutes until donuts spring back when touched; check with a toothpick.

Cool in the pan for 10 minutes, then transfer to a wire rack to cool for another 10 minutes.

Mix granulated sugar and cinnamon for coating, then brush or dip each donut in melted butter and roll in cinnamon sugar.