Preheat your oven to 350 degrees F. Generously spray a mini muffin pan with nonstick cooking spray and set aside.

In a large bowl, whisk together the all-purpose flour, baking powder, pumpkin pie spice, ground nutmeg, and salt. Set the dry mixture aside.

In a separate bowl, combine the pumpkin puree, light brown sugar, egg, milk, melted unsalted butter, and vanilla extract. Stir until the mixture is smooth and fully incorporated.

Pour the wet ingredients into the dry ingredients and stir gently until just combined. Be careful not to overmix; a few small lumps are fine.

Spoon or pipe the batter into the prepared mini muffin cavities, filling each about three-quarters full. Bake at 350 degrees F for 11 to 13 minutes, or until a wooden toothpick inserted into a donut hole comes out clean.

Remove the pan from the oven and let the donut holes cool in the pan for 5 minutes. Then transfer them to a wire rack to cool completely.

While the donut holes are cooling, place the melted butter in a small bowl. In another bowl, whisk together the granulated sugar and ground cinnamon until well blended.

Working one at a time, dip each cooled donut hole into the melted butter, ensuring it is fully coated. Then roll it in the cinnamon-sugar mixture until evenly covered.

Serve the donut holes immediately for the best texture and flavor.