Preheat your oven to 350℉. In a large mixing bowl, beat the egg for 1-2 minutes until light and fluffy.
Add the milk, oil, butter, and vanilla. Mix together until well combined. Then add the pumpkin puree and continue to mix until well combined.
Add the brown sugar and granulated sugar, and cream together with the wet ingredients.
In a separate mixing bowl, stir together the remainder of the dry ingredients. Pour them into the wet mixture and stir until just combined.
Use baking spray to grease your donut pan. Pour the batter into a plastic storage bag. Snip off the corner of the bag with scissors and carefully pipe the batter into each donut cup, filling each with about 1/4 cup of batter.
Bake for 10-12 minutes or until golden brown and a toothpick comes out clean when inserted in the donuts.
Cool the donuts in the pan for 5 minutes. Then turn out onto a wire cooling rack.
For the Cinnamon-Sugar Topping
Once cooled, brush the donuts with melted butter and dip them in a mixture of cinnamon and sugar. Serve immediatley.