Preheat oven to 350°F, and grease the doughnut pans.
Prepare the vegan egg replacer by whisking the powder with ¼ warm (not hot) water until dissolved. Set aside to rest and thicken while you continue.
Add the flours, baking powder, baking soda, sugar, spices, and salt to a mix bowl, and combine.
Once your dry mix is well combined, add in the wet ingredients: melted butter, vanilla extract, vegan egg replacer, maple syrup, and milk. Stir to combine.
Pipe batter into baking pans. The batter will be quite thick. The consistency is almost more like banana bread or muffins. That's why I find it easiest to scoop it into a pastry bag, then pipe it into your greased doughnut pan. However, you can also carefully spoon it in, then smooth it out with a wet finger. Bake doughnuts for approximately 12 minutes, or until toothpick test reveals doneness. Then, remove from oven to cool on a wire rack. Review the notes included in the above blog post about how to accomplish this without breaking the doughnuts.