Put the butter in a microwave-safe bowl and melt it in the microwave. Add 1 cup brown sugar and stir until combined. Pour the mixture evenly over the bottom of 9x13–inch baking dish. In a large bowl, whisk eggs, milk, 1 tablespoon powdered sugar, and vanilla. Place toasted bread in a single layer in the dish so that it covers the bottom. Pour half the egg-milk mixture over the entire layer of toasted bread. In a small bowl, combine the 3 tablespoons of brown sugar and 2 teaspoons of cinnamon. Sprinkle half the mixture over the layer of toasted bread. Arrange the second layer of bread and pour the rest of the egg-milk mixture over the bread. Sprinkle on the rest of the sugar and cinnamon. Cover the baking dish with aluminum foil and place in the refrigerator overnight. In the morning, preheat the oven to 350º F. Place the baking dish on the counter while the oven is preheating. When the oven is heated, cover the baking dish with aluminum foil and place it in the oven. Bake for 30 minutes. Remove the foil and bake for 15 minutes more or until the top is crispy and golden brown and the inside is soft. Sprinkle with powdered sugar. Serve with maple syrup.