Preheat the oven to 375 degrees. Grease a donut pan or use non-stick donut pan without greasing.
Mix flax and water to make your flax egg and set aside for 5 minutes or until thick.
Mix dry ingredients in a bowl (gluten-free flour, baking powder, baking soda, salt, sugar, cinnamon, pumpkin pie spice).
Mix wet ingredients in a bowl (flax egg, maple syrup, milk, applesauce, vanilla) and then combine with the dry ingredients. Mix until there are no lumps.
Spoon into donut pan, you should get about 6 donuts. Bake for 10 minutes.
Mix cinnamon sugar topping then immediately after baking, roll the donuts in it! Serve immediately! Best when fresh.