Preheat the oven to 350F. Grease a donut pan with butter.
Add the brown sugar, egg, pumpkin puree, and milk to a large bowl, and whisk to combine. Add the flour, baking powder, cinnamon, salt, nutmeg, cloves, and ginger, and whisk just until combined, being careful not to over-mix.
Transfer the batter to the donut pan, and smooth it out. Bake until a toothpick inserted in the center comes out clean, about 8 to 10 minutes. Cool to room temperature.
For the Glaze:
Once the donuts are cool, whisk together all ingredients for the glaze in a small bowl, adding more water ½ teaspoon at a time if necessary to achieve the right pour-able consistency.
Dip the top of each donut in glaze, and place the glazed donuts on a wire rack set on top of a baking tray. Let the glaze set before serving.
Notes
Recipe Yield and Serving Size: I get 8 donuts out of this recipe, for a total of 4 servings (with 2 donuts per serving).
Storage: Like most donuts, these are best eaten the same day they're made. However, you can store them wrapped at room temperature for up to 2 days.