Preheat the Oven. Preheat your oven to 350°F. Grease a donut pan and set it aside.
Mix the Dry Ingredients. In a large bowl, whisk together the flour, brown sugar, granulated sugar, baking powder, salt, pumpkin pie spice, cinnamon, nutmeg, and ginger.
Prepare the Wet Ingredients. In another bowl, whisk together the pumpkin puree, eggs, milk, melted butter, and vanilla extract until smooth and well combined.
Combine and Fill. Gradually add the wet ingredients to the dry ingredients, stirring until just combined. Be careful not to overmix. Spoon the batter into the prepared donut pan, filling each cavity about 2/3 full.
Bake the Donuts. Bake in the preheated oven for 12-15 minutes, or until a toothpick inserted into the center of a donut comes out clean. Allow the donuts to cool in the pan for a few minutes before transferring them to a wire rack to cool completely.
Make the Glaze. In a small bowl, whisk together the powdered sugar, milk, and vanilla extract until smooth. If the glaze is too thick, add a bit more milk until you reach your desired consistency.
Glaze the Donuts. Once the donuts are completely cool, dip the tops into the glaze and return them to the wire rack to set. For an extra touch, sprinkle some cinnamon sugar over the glaze before it sets.
Serve and Enjoy. Enjoy your baked pumpkin donuts with a warm cup of coffee or a cozy fall beverage.