Spray a mini muffin pan well with non-stick cooking spray and set aside.
In a large bowl, whisk together the flour, baking powder, pumpkin pie spice, nutmeg, and salt.
In a separate bowl, mix together the pumpkin puree, brown sugar, egg, milk, unsalted butter, and vanilla until fully combined.
Add the wet ingredients to the dry ingredients and mix wel.
Spoon the batter into the mini muffin cavities about 3/4 of the way full. Bake at 350 degrees for around 10 minutes or until a wooden toothpick inserted into the donut hole comes out clean.
Remove from the oven and let cool in the pan for 5 minutes. Remove the donut holes from the pan to a wire rack to cool.
Meanwhile, add the melted butter to a small bowl. Add the cinnamon and sugar to a separate bowl and mix together well.
Take each donut hole and dunk it into the melted butter, making sure it is fully coated. Then dip it into the cinnamon and sugar mixture.