Preheat the oven to 350F. Prepare a doughnut pan by spraying with non-stick cooking spray.
In a large bowl, sift together the flour, baking powder, salt, baking soda, nutmeg, cinnamon and ginger. Set aside.
In another bowl, cream together the brown sugar, butter and pumpkin. Add in the eggs, mix well, then mix in the milk and vanilla. Stir in the reserved dry ingredients.
Place the mix in a large zip-top bag. Cut off the corner and pipe into the doughnut pan.
Bake in the preheated oven until a toothpick inserted in the center comes out clean, about 10 minutes. Remove pan from oven, let rest for 5 minutes, then remove from pan and allow to cool completely on a wire rack.
Meanwhile, make the glaze: In a small bowl, whisk together the powdered sugar, maple extract, cinnamon and milk.
When the doughnuts are cool, dip them in the glaze. Return to the wire rack to allow the glaze to set.