To make the bread pudding, lightly grease a 9x13-inch baking dish with butter. Add bread cubes in an even layer in the prepared dish.

In a large bowl, whisk together eggs, cream, milk, sugar, vanilla, and salt until well combined. Pour the custard over the bread cubes evenly, pressing the cubes down to ensure they are submerged in the liquid.

Cover and refrigerate for 30 minutes, up to 2 hours.

When ready to bake, preheat oven to 350˚F. Uncover and bake until set in the center, puffed, and golden, about 45 minutes.

While the bread pudding bakes, make the creme anglaise. Add half and half and vanilla bean to a medium saucepan over medium low heat. Cook until small bubbles appear around the rim, about 5 minutes.

In a separate medium bowl, whisk together sugar and egg yolks until combined. Add half of the hot half-and-half mixture to the egg yolk mixture in a slow steady stream, whisking constantly.

Pour the mixture back into the saucepan and cook over medium heat, stirring constantly, until thickened, about 4 to 5 minutes. Remove sauce from heat and strain into a serving dish. Serve immediately or place in the refrigerator until ready to serve.