Preheat the oven to 375 degrees F. Combine 1 tablespoon butter, the bananas and maple syrup in a small saucepan and bring to a bare simmer over medium heat; keep warm.
Whisk the eggs, milk and sugar in a shallow dish. Put the crushed cornflakes in another shallow dish. Soak the bread in the egg mixture, turning once, about 45 seconds. (Remove before the bread is soggy.) Let the excess egg mixture drip off, then dredge the bread in the cornflakes, pressing gently to help them adhere. Set aside on a plate.
Melt 1 tablespoon butter in a large nonstick skillet over medium heat. Add half of the bread and cook until golden brown, about 3 minutes per side. Transfer to a baking sheet. Add the remaining 1 tablespoon butter to the skillet and repeat with the remaining bread. Transfer to the oven and bake until cooked through, about 10 minutes. Top with the banana syrup.