Preheat oven 350 degrees F. Spray a donut pan with cooking spray.
In a large bowl, whisk together the flour, baking powder, cinnamon, ginger, nutmeg, allspice, cloves, and salt.
In a separate large bowl, whisk together the pumpkin, brown sugar, oil, melted butter, eggs, milk, and vanilla until completely combined.
Stir the flour mixture into the pumpkin mixture, stirring until just combined (be careful not to over-mix the batter or the donuts will end up tough).
Carefully spoon the batter evenly around the circles of the donut rings. Fill each nearly to the top. Bake for about 12 minutes, until donuts spring back when gently pressed and a toothpick inserted into one comes out clean. Turn the donuts out onto a wire rack and allow to cool.
While the donuts are cooling, prepare the cinnamon sugar coating. In one bowl, melt the butter (let cool slightly) and in another bowl whisk the granulated sugar and cinnamon. Working with one donut at a time, use a pastry brush to spread a thin layer of butter onto the donut before dipping it into the cinnamon sugar, pressing and turning it to coat all sides. Repeat with the remaining donuts. The donuts will keep for up to 4 days in an airtight container at room temperature but they're especially delicious the day you bake them.