Au Jus
Make the au jus. In a small (3 qt) saucepan over medium heat, add the olive oil and shallots and cook until softened, 2 minutes. Add the garlic, rosemary, thyme, sherry vinegar and rib bones, if using, and stir. Add the beef stock and bring to a simmer. Reduce heat as needed, and cook until reduce by half, about 20 minutes. Taste for seasoning and adjust, as needed with pepper, and salt. Strain into a serving dish, and keep warm.
French Dip
In a small bowl, add the horseradish and mayonnaise, and stir to combine.
Spread the softened butter on the cut side of the rolls.
In a large skillet over medium heat, place the roll, cut-side-down, and toast until golden brown, 1-2 minutes. Remove from skillet and add the cooked prime rib with ¼ cup of the au jus or more as needed, and cook to warm the beef through, 2-3 minutes.
Spread the horseradish sauce on the toasted rolls, as desired, then fill with the prime rib, dividing evenly among the sandwiches. Serve with bowls of au jus for dipping, and additional horseradish sauce as desired. Enjoy!