Preheat oven to 350°F. Lightly coat a 9-inch square baking pan with cooking spray.
Whisk 1¼ cups oats, ½ cup all-purpose flour, ½ cup whole-wheat flour, 1½ teaspoons baking powder, 1½ teaspoons cinnamon and ½ teaspoon salt together in a small bowl.
Whisk 1¼ cups banana, 4 tablespoons peanut butter, ¼ cup milk, ¼ cup applesauce, 3 tablespoons honey, 1 egg and 2 teaspoons vanilla together in a large bowl until combined.
Fold the oat mixture into the banana mixture until just combined and no dry streaks remain; transfer to the prepared baking pan, spreading into an even layer.
Dollop the remaining 2 tablespoons peanut butter evenly on top. Using a toothpick or a paring knife, drag the peanut butter throughout the oat mixture, creating a marbled look.
Bake until the edges begin pulling away from the pan sides, about 30 minutes.
Let stand in the pan on a wire rack until cool enough to handle, about 10 minutes. Slice and serve warm.
