Preheat oven to 350°F (175°C). Grease an 8-inch square baking dish.
Heat milk, sugar, butter, cinnamon, and salt until butter melts. Let cool 10 minutes.
Arrange cubed bread in dish.
Whisk eggs and vanilla into milk mixture, then pour over bread. Rest 20–30 minutes.
Bake 40–45 minutes until golden and set. Cool slightly.
For sauce: Heat milk, cream, brown sugar, and butter until steaming.
Dissolve cornstarch in water or bourbon, whisk into hot mixture until thickened. Stir in vanilla.
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