Prep the pan: Preheat oven to 350°F and lightly grease a 24-cup mini muffin pan.
Mix dry ingredients: Whisk together flour, baking powder, pumpkin pie spice, cinnamon, and salt.
Mix wet ingredients: Whisk pumpkin puree and brown sugar until smooth. Add egg, milk, oil, and vanilla; whisk until combined.
Make the batter: Add dry ingredients to the wet mixture and gently fold until just combined. Do not overmix.
Fill the pan: Spoon about 1 tablespoon batter into each mini muffin cup, filling about two-thirds full.
Bake: Bake for 10–12 minutes, or until the tops spring back and a toothpick comes out clean or with a few moist crumbs.
Cool briefly: Let cool in the pan for 3–5 minutes, then transfer to a wire rack. Mix cinnamon and sugar in a shallow bowl.
Coat: Brush warm donut holes lightly with melted butter, then roll in cinnamon sugar until evenly coated. Serve warm.
