Preheat the oven to 425°F and generously butter a 9x13-inch baking dish; set it aside.
In a small saucepan over medium heat, melt the butter completely, then incorporate the brown sugar, stirring continuously until the mixture is smooth and fully blended. Evenly spread this syrupy layer across the base of the prepared baking dish.
Distribute the cubed French bread over the brown sugar-butter mixture, ensuring a uniform layer.
In a mixing bowl, whisk the eggs together with the milk, vanilla extract, and 1 teaspoon of cinnamon until fully combined. Pour this custard mixture over the bread cubes, ensuring thorough saturation.
Sprinkle the remaining teaspoon of cinnamon along with the tablespoon of brown sugar across the top.
Transfer the dish to the preheated oven and bake for 25 to 30 minutes, or until the top develops a golden-brown crust.
Remove from the oven and, if desired, finish with a dusting of powdered sugar before serving.