Preheat oven to 350°F (175°C). Butter a 9x13-inch baking dish and arrange the bread cubes in an even layer.
In a large bowl, whisk together eggs, milk, 1 cup heavy cream, granulated sugar, 2 teaspoons vanilla extract, cinnamon, and salt until smooth and well combined.
Pour the custard mixture evenly over the bread cubes, pressing down gently with a spatula to ensure all pieces are soaked. Let stand for 20-30 minutes at room temperature.
Place the baking dish inside a larger roasting pan. Pour hot water into the roasting pan until it reaches halfway up the sides of the baking dish to create a water bath.
Bake for 45-50 minutes, until the top is golden brown and the center is set but still slightly jiggly. A knife inserted 2 inches from the edge should come out mostly clean.
While the pudding bakes, make the bourbon sauce: Melt butter in a medium saucepan over medium heat. Stir in brown sugar and 1/2 cup heavy cream, whisking constantly until the mixture comes to a gentle boil.
Reduce heat to low and simmer the sauce for 3-4 minutes, stirring occasionally, until slightly thickened. Remove from heat and stir in bourbon and 1 teaspoon vanilla extract.
Remove the pudding from the oven and let it cool for 10 minutes. Serve warm portions drizzled generously with the bourbon vanilla sauce.
