Prepare the Baking Dish: Grease a 9×13-inch baking dish with butter. In a bowl, mix ¼ cup brown sugar and 1 teaspoon cinnamon. Sprinkle half of the cinnamon sugar mixture over the bottom of the baking dish.

Make the Cream Cheese Filling: In a bowl, use an electric mixer to whip the cream cheese for 1 minute. Add the heavy cream and vanilla, then gradually increase the speed to high. Continue whipping until fluffy, 1-2 minutes.

Stuff the Bread: Make a 1-inch slit at the top of each slice of bread, then carefully create space inside the bread without poking through to the other side. Spread the cream cheese mixture inside each slice and press to enclose. Save the leftover cream cheese for serving.

Prepare the Egg Mixture: In a large bowl, whisk together eggs, milk, vanilla, and salt. Submerge each piece of bread into the egg mixture, allowing the bread to sit for at least a minute to soak up the eggs. Arrange the bread slices in the prepared baking dish. Pour the remaining egg mixture over the bread slices and sprinkle the rest of the cinnamon sugar on top. Cover and refrigerate for 30 minutes or overnight.

Bake the French Toast: Preheat the oven to 375°F (190°C). In a bowl, mix the remaining 1/3 cup brown sugar, 1 ½ teaspoons cinnamon, flour, and melted butter. Sprinkle this topping evenly over the bread slices.

Bake and Serve: Cover and bake for 25 minutes, then remove the foil and bake for another 20-25 minutes or until the French toast is deeply golden.

Serve the baked French toast warm, topped with any additional whipped cream. Enjoy!