Whisk the sour cream, horseradish, mayonnaise, Dijon, Worcestershire, salt, and pepper in a small bowl until smooth. Refrigerate.

Melt half the butter in a skillet over medium heat. Sauté the onion with a pinch of salt until soft and golden, about 8 to 10 minutes. Set aside.

Heat the broiler and position a rack 6 inches from the heat. Split the rolls, place them cut side up on a baking sheet, and broil 1 to 2 minutes until lightly toasted.

Melt the remaining butter in the same skillet over low heat. Add the sliced prime rib and warm gently for about 2 minutes, stirring once, just until no longer cold.

Spread the horseradish sauce on both cut sides of each roll. Layer the warm prime rib, onions, and a slice of provolone on the bottom halves. Broil open-faced about 2 minutes until the cheese melts and edges crisp. Warm the beef broth in a small saucepan. Close the sandwiches, slice on a diagonal, and serve with small bowls of warm au jus.