Caramel, Apple, And Cinnamon Breakfast Casserole

Ingredients

• 10 large eggs
• 2 cups well-shaken buttermilk
• 2 cups heavy cream
• 1 cup unfiltered apple juice or apple cider
• 1 cup packed light brown sugar
• 1 vanilla bean, split lengthwise and scraped, seeds reserved
• 1 1/2 teaspoons ground cinnamon
• 1 teaspoon fine salt
• 1 (1-pound) day-old loaf french bread, cut into 1-inch cubes (about 12 cups)
• butter, for coating the baking dish
• 1 1/2 pounds apples, such as rome, pink lady, or other sweet apples (about 3 medium)
• 1 cup dulce de leche