Preheat the oven to 350 degrees Fahrenheit. Grease a 12-cup standard-size muffin tin with non-stick cooking spray or vegetable shortening.
In a small bowl, stir together 2 tablespoons flax meal and 6 tablespoons water. Let sit for 5 minutes to thicken.
In a large bowl, whisk together the flours, baking soda, and salt.
In a medium bowl, mash the bananas. Stir in the brown sugar, applesauce, vegetable oil, vanilla extract, and flax/water combination.
Make a well in the middle of the dry ingredients and pour in the wet ingredients. Stir just until the ingredients are incorporated. Batter will be thick.
Divide batter between 12 muffin cups. If you prefer larger muffins with big, domed crowns, divide the batter between 9 muffin cups instead of all 12.
Sprinkle remaining 2 teaspoons flax meal over the tops.
Bake for 18 - 22 minutes, until a toothpick inserted into the center of the muffins comes out clean.
Remove from oven and place tin on a rack to cool for about five minutes. Transfer individual muffins to a wire rack to let cool completely.
These muffins keep for 3 - 4 days in an airtight container at room temperature, or freeze in a zipper bag.