For the bread pudding: Position an oven rack in the middle of the oven and preheat to 350 degrees F. Butter a 2-quart baking dish.
Scatter the bread cubes on a baking sheet. Drizzle with the melted butter and toss to coat. Bake, stirring halfway through, until the bread is golden brown and crunchy, 10 to 15 minutes. Let cool completely.
Meanwhile, follow the package directions for microwaving and salting the pretzels (don't use all the salt). Quarter each pretzel.
Whisk together the milk, cream, sugar, vanilla, whole eggs and yolks in a medium bowl.
Scatter the bread cubes in the prepared baking dish. Top with the pretzel pieces (turning some over to show off the nicely browned bottoms) and then nestle in the caramel candy halves. Pour the custard over the mixture. Cover with foil and set aside at room temperature for 20 minutes.
Bake until the bread pudding is set with a slight jiggle in the center, 45 to 55 minutes. Let rest for at least 15 minutes before serving.
For the caramel sauce: Meanwhile, combine the caramels, butter and cream in a small microwave-safe bowl. Microwave, stirring halfway through, until the caramels and butter melt together, about 2 minutes. Whisk until smooth and thick. (The caramel sauce can be made ahead of time and then reheated to loosen up for serving.)
Drizzle the bread pudding with the caramel sauce and sprinkle with some pretzel salt before serving.
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