Spray a 9×13-inch baking dish generously with nonstick cooking spray.
In a medium bowl, mix together ⅔ cup brown sugar and 1 heaping teaspoon cinnamon. Set aside.
In another medium bowl, whisk together 5 large eggs, 1½ cups milk, and 1 teaspoon vanilla extract until well combined.
Arrange 5–6 slices of thick bread in an even layer in the bottom of the prepared baking dish.
Sprinkle half of the brown sugar and cinnamon mixture evenly over the bread.
Layer the remaining 5–6 slices of bread on top, then sprinkle with the remaining brown sugar mixture.
Slowly pour the egg and milk mixture evenly over the bread, making sure all pieces are moistened.
Cover the dish tightly with foil and refrigerate overnight.
When ready to bake, preheat the oven to 350°F.
Bake the French toast covered for 30 minutes.
Remove the foil and continue baking for 15–20 minutes, or until the top is golden and the center is set.
Serve warm with maple syrup.