Preheat oven to 375F with the rack in the middle. Butter a 3-4qt baking dish.
Make the bread pudding by whisking together in a large bowl the eggs and half and half until frothy. Add in the brown sugar, cinnamon, and vanilla bean seeds. Whisk until well combined.
Add in the bread and gently mix just to coat. Add in the apples and caramel pieces and fold to combine being careful not to break up the bread. Gently pour the mixture into the baking dish. You want to be sure you have about an inch of room above as this will inflate.
Place the baking dish on a rimmed baking sheet to catch any drippings.
Bake for 35-45 minutes or until the top has a slight give when pressed down, the apples are soft and the center is set.
Vanilla Butterscotch Sauce
While the bread pudding is baking make the sauce by adding the brown sugar, flour, and half and half to a medium saucepan over medium heat.
Whisk together until it begins to bubble and thicken to where it coats the back of a spoon, ~7-10 minutes. Remove from heat and stir in the butter and vanilla. Drizzle over the bread pudding while both are hot. Top with Vanilla Bean or Butter Pecan Ice Cream if desired