Preheat oven to 375 degrees. Butter an 8-inch square baking dish.
Combine the oats, half the nuts, sugar, baking powder, cinnamon, and salt in a bowl. In another bowl, whisk the milk, egg, half the butter, and the vanilla.
Arrange bananas in a single layer on the bottom of the coated baking dish. Sprinkle with two-thirds of the berries, then cover with the oat mixture. Slowly drizzle milk mixture over the oats. Gently tap dish on a work surface to distribute liquid. Scatter remaining berries and nuts across the top.
Bake for 35 to 40 minutes, until the top is nicely golden and the oat mixture has set. Let cool slightly. Drizzle with remaining melted butter and maple syrup.