Preheat the oven to 350°F. Prepare 2 donut pans with butter or spray with nonstick cooking spray. Set aside.
In a large bowl, whisk together the flour, baking powder, salt, cinnamon, pumpkin pie spice and nutmeg. Set aside.
In a medium bowl, whisk together the melted butter, brown sugar and egg. Then add the pumpkin puree, milk and vanilla and whisk until well combined. Add the wet ingredients to the dry ingredients and mix with a spatula until combined.
Transfer the batter into the prepared donut pans. Bake until a toothpick inserted in the center comes out clean, about 8-10 minutes. Allow the donuts to cool in the pans for 5 minutes, then remove to cool on a wire rack.
While the donuts cool, prepare the topping: in a bowl combine the sugar, pumpkin pie spice and cinnamon.
Once donuts are cool enough to handle, use a pastry brush to coat each donut with melted butter, then dip each side of the donut into the spice sugar mixture.