Preheat oven to 350ºF. Grease a 5x9-inch glass baking dish with a little of the oil. Set aside. Combine flour, baking powder, baking soda and salt in a large bowl. Stir to mix thoroughly. In a separate bowl, mix eggs, bananas, sugar, oil and vanilla. Add banana mixture to flour mixture and stir with a wooden spoon until just combined. Fold in mango and walnuts. Transfer batter to baking dish.

Bake in center of the oven until a wooden pick inserted in the middle of the bread comes out clean, about 50 minutes (check at 45 minutes—oven temperatures vary). Transfer baking dish to a wire cooling rack and let cool for 15 minutes. Carefully work around the edges of the bread with a thin, flexible baking spatula to loosen it and turn it out onto the rack. Let the bread cool completely before serving (that was the hardest part of this recipe).