Preheat oven to 350℉ and grease an 8½ x 4½-inch loaf pan or a 9 x 5-inch loaf pan with cooking spray.
In a medium bowl, combine flours, oats, baking powder, baking soda, cinnamon, and salt.
In another bowl, combine the eggs, mashed bananas, brown sugar, oil, and vanilla. Stir until just moistened. Add this to the dry ingredients and stir until just combined. Transfer the batter into the prepared loaf pan and top with toasted walnuts. Bake for 50-55 minutes
Bake at 350 degrees for 50 to 55 minutes or until a tester inserted in the middle comes out mostly clean. If the bread browns too quickly, tent with foil halfway through baking. Cool in the pan for 10 minutes before removing from the pan and slicing.
Notes
Flour: While this recipe combines all-purpose and whole wheat flour, you can use only all-purpose flour. Adjust the measurement to 1 ½ cups and eliminate the whole wheat flour.