Preheat your oven to 350°F (175°C) and grease your donut pan.
In a large mixing bowl, combine the dry ingredients: gluten-free flour, baking powder, baking soda, cinnamon, nutmeg, ginger, and salt.
In another bowl, mix the wet ingredients: pumpkin puree, granulated sugar, brown sugar, applesauce, vegetable oil, eggs, and vanilla extract until smooth.
Gradually add the dry mixture to the wet mixture, stirring gently until just combined.
Fill each cavity of the donut pan about two-thirds full with the batter.
Bake the donuts for 15 to 18 minutes, checking for doneness with a toothpick.
Allow the donuts to cool in the pan for 5 minutes before transferring them to a wire rack to cool completely.