Preheat the oven to 350 degrees F. Spray a muffin tin with cooking spray and set aside.
In a large bowl combine pumpkin puree with both sugars, mixing to combine. Add apple sauce, oil, and vanilla extract and stir until smooth. Fold dry ingredients into the wet ingredients until a uniform batter has formed. Be careful not to over-mix.
Fill muffin molds 2/3 of the way full. Bake for 20 minutes or until a knife inserted in the middle comes out clean.
To top the muffins, combine the cinnamon and sugar in a small bowl. Melt the butter in the microwave or on the stovetop. Lightly brush each top with melted butter and sprinkle with cinnamon and sugar.
Serve immediately or store in an airtight container at room temperature for up to 5 days.