Preheat the oven to 350° and grease the doughnut pan if it’s not a non-stick pan
In a large mixing bowl whisk the dry ingredients together and set aside.
In a small bowl add the applesauce and 1 teaspoon baking powder and whisk until it bubbles and becomes frothy. Add the brown sugar and mix until well combined. Add the pumpkin puree, vanilla, milk, and the maple syrup and mix until well combined.
Pour the wet ingredients into the dry and stir until just combined. Don't overwork it or you'll get a tough doughnut. Add more milk if the batter is too stiff. It should be firm but not difficult to stir.
Bake for approximately 20 to 25 minutes or until a toothpick comes out clean. Cool on a wire rack for 10 minutes and then remove from the pan and place on the rack until completely cool
For the icing:
In a medium bowl stir the confectioner’s sugar, cocoa, cinnamon, and milk together until smooth and creamy. The texture should be between frosting and a glaze. Add more milk if needed.
When the doughnuts are completely cool frost the doughnuts.