1. For the Bread Pudding:
   Step 1: Preheat the oven to 350°F (175°C). Lightly grease an 8-inch square baking dish with butter.
2. Step 2: Prepare the custard base: In a medium saucepan over medium heat, combine milk, granulated sugar, butter, cinnamon, and salt. Stir occasionally until the butter melts. Remove from heat and let cool for 10 minutes.
3. Step 3: Assemble the pudding: Place bread cubes in the prepared baking dish. Once the milk mixture is lukewarm, whisk in eggs one at a time, followed by vanilla extract. Pour the custard evenly over the bread, ensuring all pieces are coated. Allow the mixture to rest for 20–30 minutes to absorb the custard.
4. Step 4: Bake: Transfer the dish to the preheated oven and bake for 40–45 minutes, or until the top is golden brown and a knife inserted into the center comes out clean.

For the Vanilla Sauce:

1. Step 1: Heat the base: In a medium saucepan over medium heat, combine milk, cream, brown sugar, and butter. Stir until the sugar dissolves and the mixture begins to steam (5–7 minutes).
2. Step 2: Thicken the sauce: Dissolve cornstarch in water, bourbon, or rum. Gradually whisk the cornstarch slurry into the steaming milk mixture. Cook, stirring constantly, until thickened to a velvety consistency (2–3 minutes).
3. Step 3: Finish the sauce: Remove from heat and stir in vanilla extract and a pinch of salt, if desired.