Place the unsalted butter in a microwave-safe bowl. Microwave it in 20-second intervals, stirring after each interval, until the butter has melted completely.
Stir the 1 cup of packed light brown sugar into the melted butter until the two ingredients are thoroughly combined.
Grease a 9×13-inch baking dish. Pour the brown sugar and butter mixture across the bottom, spreading it into an even layer.
Combine the eggs, whole milk, and vanilla extract in a mixing bowl. Beat until the mixture is smooth and evenly blended.
Set the prepared custard aside while arranging the bread.
If necessary, slice the Texas toast before assembling the casserole.
Arrange one layer of bread in the prepared baking dish, trimming individual pieces when needed so that the brown sugar-butter base is fully covered.
Evenly spoon 1 cup of the prepared egg custard over this first bread layer.
In a small bowl, combine the 2 tablespoons of light brown sugar with the ground cinnamon.
Scatter half of the cinnamon-brown sugar mixture evenly over the custard-soaked bread.
Arrange a second layer of Texas toast over the first layer. Pour or spoon the remaining egg custard evenly across the bread.
Finish by sprinkling the remaining cinnamon and brown sugar mixture over the surface. Gently press the bread downward so it absorbs the custard more thoroughly.
Transfer the assembled casserole to the refrigerator and leave it overnight, allowing the bread sufficient time to absorb the custard.
If desired for a richer finished texture, allow the refrigerated casserole to stand at room temperature while the oven comes to temperature.
Position the casserole on the lower-middle oven rack. Bake for 40–45 minutes in total, keeping the dish covered during the first 30 minutes.
Remove the covering for the remaining baking time so that the upper surface can become golden with a lightly crisp finish.
Remove the baked French toast casserole from the oven and allow it to cool for several minutes.
Dust the surface generously with powdered sugar.
Cut into portions and serve, making certain to spoon some of the sticky caramelized brown sugar sauce from the bottom of the baking dish over each serving.
Drizzle with pure maple syrup, if desired.