Preheat the oven to 350°F (175°C). Coat a 9-by-5-inch loaf pan with nonstick cooking spray.
Whisk the flour, baking powder, baking soda, and salt together in a medium bowl.
Combine the mashed banana and cornflakes in another bowl. Let stand for 5 minutes, until the cereal softens.
Beat the softened butter and sugar in a large bowl until light and creamy. Beat in the eggs one at a time.
Stir in the banana-cornflake mixture and chopped cashews. Add the dry ingredients and fold just until no dry flour remains.
Spread the batter evenly in the prepared loaf pan. Bake for about 1 hour, until a toothpick inserted in the center comes out clean.
Cool in the pan for 10 minutes, then turn the loaf onto a wire rack and cool before slicing.