Heat oven to 425°F, line two rimmed sheet pans with parchment and brush with half the butter.
Cut each bread slice lengthwise into two thick sticks.
Whisk eggs, milk, sugar, vanilla, cinnamon and salt in a shallow dish.
Dip each stick briefly on all sides, let excess custard drip away and arrange without touching on the pans.
Brush the tops with remaining butter and bake for 10 minutes.
Turn the sticks and bake 8 to 10 minutes more until evenly golden and set in the center.
Serve hot with small portions of maple syrup for dipping.