Preheat oven to 375°F. Lightly spray a mini muffin tin with cooking spray and set aside.
Combine dry ingredients (flour, brown sugar, baking powder, pumpkin pie spice, and salt) in a small mixing bowl and set aside.
In a large mixing bowl, add egg and beat with whisk. Add in pumpkin puree, milk, and vanilla, whisking until combined.
Add the flour mixture to the mixing bowl, stirring with a rubber spatula until combined. Stir in melted butter, until everything is well mixed.
Scoop about 1 Tbsp of the batter into each muffin cavity.
Bake for 10-12 minutes, until a toothpick inserted into the center comes out clean or with a few moist crumbs.
Let donut holes cool on a wire cooling rack.
While donuts are cooling, make the cinnamon sugar topping by combining the granulated sugar and ground cinnamon in a shallow bowl.
Melt the butter and set aside.
Dip cooled donut holes, one at a time, into the melted butter (shaking off the excess), then into the cinnamon sugar mix, rolling them to coat.