Preheat the oven to 350°F.
Line two baking sheets with silicone baking mats.
In a large bowl, stir together flour, sugar, baking powder, pumpkin pie spice, and salt.
In a separate bowl, stir together the remaining ingredients (buttermilk, pumpkin puree, vanilla, egg, and butter).
Stir the wet ingredients into the dry ingredients. Stir just until well mixed. The batter will be thick.
Scoop 1 tablespoon size amounts and shape them into balls using your hands. You’ll want to grease your hands for this step.
Place balls two inches apart on baking sheets. Bake one sheet at a time.
Bake for 14 to 15 minutes or until a toothpick inserted in the middle of the donut hole comes out clean.
Let cool for 5 minutes before adding the topping.
Topping
Place half of the donut holes in a large, resealable food storage bag. Pour half the melted butter into the bag and shake well to coat all donut holes. Remove the donut holes from the bag and set them aside. Repeat the steps with the rest of the donut holes and melted butter.
In a small bowl, stir together cinnamon and sugar. Pour the cinnamon sugar mixture into a clean food storage bag, add half the buttered donut holes, and shake well to coat. Remove from the bag and set on the baking tray to cool. Repeat with the other half of the donut holes.
Remove the donut holes from the bag and serve warm.