Preheat oven to 350°F. Grease and flour a loaf pan and set aside. In a large bowl, stir together dry ingredients including the oats and cinnamon. In a smaller bowl, mash bananas with a potato masher or fork. Add oil and whole egg and mix thoroughly. Add the wet ingredients to the dry and mix well. Batter will be fairly thick.
In a medium sized bowl, with an electric hand mixer, beat the egg whites until medium stiff peaks form. Fold the egg whites into the batter in three additions.
Pour batter into pan and bake until top of loaf is firm to touch, 45 to 50 minutes. Remove from oven and allow to cool in pan for 5 minutes. Flip out and cool on a wire rack for another 10 minutes. Slice loaf into 10 equally sized slices.