Preheat the oven to 350° F. Grease a donut pan with non-stick cooking spray.
Mix the flour, brown sugar, pumpkin pie spice, baking powder, baking soda and salt in a large bowl with a large spoon. Set aside.
In a different mixing bowl, add the pumpkin puree, eggs, maple syrup, melted butter, and vanilla extract. Mix until well combined.
Pour the pumpkin mixture into the dry ingredients bowl. Combine the two mixtures together until they form a thick batter.
Place the donut batter in a gallon-sized plastic bag or piping bag. Snip a hole in the corner and pipe the donut batter into the prepared donut pan molds.
Bake the donuts for 17-18 minutes in the preheated oven.
While the donuts bake, make the pumpkin spice topping. Mix together the granulated sugar, ground cinnamon, and pumpkin pie spice in a small bowl.
Allow the donuts to cool on a cooling rack until they are able to be handled, about 5-10 minutes. Brush a thin coating of melted butter on each donut and dip the buttered side in the cinnamon-sugar topping. Serve warm and enjoy!