Preheat the oven to 350°F Coat a 9X5 inch loaf pan, or 2 mini pans, with cooking spray.
In a bowl or a zipper lock bag, mix the flours with the baking soda, baking powder, salt, and cinnamon, if using. Set aside.
In a large mixing bowl, mix the sugar and oil with a wooden spoon until well combined. Mix in the egg whites, banana and cauliflower purees, and vanilla. Add the flour mixture and mix just until combined.
Pour the batter into the loaf pan. Bake until a toothpick inserted into the center comes out clean, 55 to 60 minutes for the larger loaf, 25 to 30 minutes for the mini loaves. Let cool on a rack for 5 minutes, then turn the bread out of the pan to cool before serving.