Preheat oven to 350 degrees. Spray a donut pan (6-count pan) with nonstick cooking spray and set aside. In a large mixing bowl, whisk together the flour, baking powder, pumpkin pie spice, nutmeg, and salt. In a separate mixing bowl, mix together the brown sugar, pumpkin, milk, egg, butter, and vanilla extract. Mix well. Add the dry ingredients to the wet ingredients, lightly sitrring until just combined.
Place donut filling into an icing bag or a zip-top bag. If you are using a zip-top bag, cut an opening for piping the mixture into the donut pan. Pipe the batter evenly between all 6 donut cavities.
Bake at 350 degrees for 8 minutes or until a toothpick inserted into the donuts comes out clean.
Remove from oven and allow to cool for 3 minutes, or until you can easily handle the donuts. Remove the donuts to a cooking rack placed over wax paper and continue to allow the donuts to cool while you make the icing.
In a medium bowl, mix together the powdered sugar, cinnamon, maple syrup, milk, and salt until well combined. If the icing is a little too thick, add a splash of milk to thin it out.
Dip the tops of each cooled donut into the glaze and transfer back to the wire rack to let the glaze harden for about 10-15 minutes. I like to dip them a second time for a thicker coat of icing. Serve and enjoy!