Preheat the oven to 350°F (175°C) and lightly grease two 6-cavity donut pans.
In a large mixing bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, ginger, cloves, and nutmeg.
In a separate medium bowl, whisk the pumpkin puree, brown sugar, granulated sugar, vegetable oil, eggs, and vanilla extract until emulsified.
Gradually fold the wet ingredients into the dry ingredients using a spatula until just combined; do not overmix.
Transfer the batter into a piping bag or a large plastic bag with the corner snipped off.
Pipe the batter into the prepared donut pans, filling each cavity approximately three-quarters full.
Bake for 10 to 12 minutes, or until the donuts spring back when lightly touched and a toothpick comes out clean.
Cool the donuts in the pan for 5 minutes, then invert them onto a wire cooling rack.
In a small bowl, combine the coating sugar and cinnamon; place the melted butter in a separate small bowl.
Dip each warm donut into the melted butter, then immediately dredge in the cinnamon-sugar mixture to coat thoroughly.