Preheat oven to 375°F. Lightly coat a 9-inch-square baking dish or pan with cooking spray.
Whisk 2 eggs, 3½ tablespoons brown sugar, 1 tablespoon vanilla, 1 teaspoon baking powder, ½ teaspoon cinnamon,¼ teaspoon salt and 1 cup mashed banana in a large bowl until evenly combined. Add 2 cups milk; whisk until smooth. Stir in 2½ cups oats and ⅓ cup walnuts.
Transfer to the prepared baking dish; sprinkle with the remaining ½ cup walnuts.
Bake until just set in the center and the top is golden brown, 45 to 50 minutes. Let cool in the baking dish on a wire rack for 10 minutes before serving.
