Preheat the oven to 350°F (175°C). Grease a 6-cavity doughnut pan and set aside.
In a medium bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, nutmeg, ginger, and cloves.
In a large bowl, whisk together the pumpkin puree, granulated sugar, brown sugar, eggs, milk, oil, and vanilla extract until smooth.
Gradually add the dry ingredients to the wet ingredients, stirring until just combined. Do not overmix.
Transfer the batter to a piping bag or a zip-top bag with the corner snipped off. Pipe the batter into the prepared doughnut pan, filling each cavity about ¾ full.
Bake for 12-15 minutes, or until a toothpick inserted into the doughnuts comes out clean. Cool in the pan for 5 minutes before transferring to a wire rack.
In a small bowl, mix the granulated sugar and cinnamon.
While the doughnuts are still warm, lightly brush them with melted butter (optional) and toss them in the cinnamon-sugar mixture until fully coated.