Preheat the oven to 400 degrees. Spray a donut pan with cooking spray.
In a large bowl, whisk together the flour, brown sugar, baking powder, salt, and apple pie spice. Set aside.
In a medium bowl combine the eggs, milk, pumpkin puree, butter, and vanilla. Mix well.
Pour the egg mixture into the flour mixture and stir until just mixed.
Place the batter in a zip top baggie and fill each donut well two-thirds full being careful how you fill it as it will keep it's shape.
Bake for 10-12 minutes or until donut springs back when touched.
Let the donuts cool in pan for 5 minutes. Remove from pan and cool completely on a wire rack.
In a small bowl combine all the ingredients for the Autumn Spiced Sugar, except the butter.
Melt the butter in a small bowl. Dip each donut into the butter and then dip into the sugar.
Let sit for 10 minutes then enjoy!