Preheat oven to 350°F (176°C). In a large bowl, combine the dry ingredients, sifting in the baking powder and baking soda. Stir through until well combined. In another bowl, combine applesauce, maple syrup, non-dairy milk, and vanilla, and mix together. Add the wet mixture to the dry mixture, and gently fold and mix through, until just combined (do not overmix). Spoon the mixture into a muffin pan lined with cupcake liners (this will fill 12 muffins quite full). Bake for 21-23 minutes, or until a toothpick inserted in the center comes out clean. (See notes above about cooling to help remove from liner.) Makes 12 large muffins.