Preheat oven to 375 degrees F (190 degrees C). Grease an 8-inch square baking pan.
Combine oats, 1 cup flour, brown sugar, cinnamon, salt, and baking powder together in a bowl. Beat milk, applesauce, honey, peanut butter, and vanilla extract together in a large bowl until smooth; add eggs and mix well. Mix oats mixture into milk mixture until batter is just combined; stir in bananas. Pour 1/2 of the batter into the prepared baking pan.
Bake in the preheated oven until partially cooked, about 5 minutes. Remove pan from oven and cool completely.
Mix milk chocolate chips, semisweet chocolate chips, and 1 teaspoon flour together in a bowl until chips are coated in flour, adding more flour if needed. Spread coated chips over the cooled loaf and top with remaining batter.
Bake in the oven until loaf is cooked through and lightly browned on top, 35 to 45 minutes.
