Pour melted butter into an 11×15-inch baking dish. Sprinkle brown sugar and cinnamon over the butter and top with bread slices, making sure slices are placed close together.
Mix milk, eggs, and vanilla extract in a bowl until thoroughly combined; pour over bread in the baking dish. Cover with aluminum foil and refrigerate, 8 hours to overnight.
Preheat the oven to 350 degrees F (175 degrees C).
Place the covered casserole in the preheated oven and bake for 30 minutes. Uncover, and bake until puffed and lightly golden, about 15 minutes more.
Half-and-half may be substituted for milk, if desired.
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