Instructions

1. Preheat oven to 350°F. Cut 5 (¾-inch thick) slices of bread, and place on one side of a rimmed baking sheet. Cut remaining bread into 1-inch cubes; place on other half of baking sheet. Bake 5 minutes.
2. Meanwhile, whisk eggs, egg yolks, 2 cups cream, milk, sugar, and vanilla bean paste in a large bowl; set aside.
3. Place bread slices along bottom of a 3-quart baking dish, trimming if needed to fit in one even layer. Evenly distribute diced bread on top. Pour egg mixture over bread; let stand 10 minutes.
4. Place baking dish in a large roasting pan. Pour 1-inch of hot tap water in roasting pan around baking dish; cover entire roasting pan with foil, poking a few holes in foil to allow steam to escape.
5. Bake 45 minutes; remove foil, and bake 45 minutes longer or until egg mixture is set, bread is golden brown, and a wooden pick inserted in center comes out clean.
6. Meanwhile, melt butter in a small saucepan over medium-low heat. Stir in brown sugar and rum; cook, whisking until sugar dissolves.
7. Stir in ½ cup heavy cream, and cook 2 to 3 minutes or until slightly thickened. Serve sauce over bread pudding.