Heat the oven to 350°F and butter a 9-inch square baking dish with sides at least 2 inches high. Mix the oats, baking powder, cinnamon and salt.
Whisk the mashed bananas, eggs, milk, syrup, melted butter and vanilla in another bowl.
Stir the wet mixture into the oats and fold in the walnuts. Pour into the dish and spread the oats evenly rather than leaving a mound in the middle.
Bake for 35 to 40 minutes, until the center is set, reaches 160°F and does not ripple when nudged.
Rest for 10 minutes, then cut into eight portions. Refrigerate cooled leftovers and reheat individual portions to 165°F.