Instructions

Make the bread pudding

• Position a rack in the center of the oven and heat the oven to 325°F.
• Spread the bread cubes in a single layer on a large rimmed baking sheet and toast until lightly golden, about 7 minutes. Set aside.
• In a large bowl, whisk together the cream, sugar, eggs, yolks, vanilla, and salt. Stir in the bread cubes, pressing down to submerge them in the custard. Let the bread soak for 1 hour at room temperature and up to 4 hours, covered, in the refrigerator, occasionally folding the mixture with a spatula.

Make the caramel sauce

• Meanwhile, fill a small bowl halfway with water and put a pastry brush in it; this will be used for washing down the sides of the pan to prevent crystallization. Combine the sugar, corn syrup, and 1/4 cup water in a heavy-duty 4-quart saucepan. Bring the mixture to a boil over high heat, stirring often, until the sugar dissolves and is clear, about 35 minutes. When sugar crystals begin to form on the sides of the pan, wash them down with the wet pastry brush.
• Reduce the heat to maintain a gentle boil. Don’t stir at this point, but check frequently until the sugar begins to turn a light honey color around the edges, about 10 minutes, brushing down the sides whenever necessary. Gently swirl the pan to even out the color and prevent the sugar from burning in isolated spots. Continue to cook until the sugar turns a rich red-brown color, about 2 minutes more. (Once the mixture begins to color, it will darken very quickly, so keep an eye on it.) Remove from the heat.
• Carefully stir in the cream with a wooden spoon; the caramel will bubble and steam. Continue to stir until any solidified caramel melts. (If it doesn’t, set the pan over medium-low heat and stir gently until the caramel is completely smooth.) Stir in the butter and salt. Let cool to room temperature before serving.

Assemble

• Generously butter a 9×13-inch baking dish. In a small bowl, stir together the granulated sugar, raw sugar, and cinnamon.
• Choose a roasting pan large enough to accommodate the prepared baking dish with an inch or 2 of space on all sides.
• Pour the bread mixture into the prepared baking dish and sprinkle evenly with the cinnamon sugar. Cover the dish with aluminum foil, place in the roasting pan, and transfer to the oven. Pour 1 inch of boiling water around the baking dish and bake until the custard is set, about 30 minutes. Remove the foil and continue baking until the top is crisp, about 20 minutes more.
• Remove the bread pudding from the roasting pan and let cool for at least 20 minutes. Serve drizzled with the caramel sauce and sprinkled with coarse sea salt.