For the prime rib: Preheat the oven to 450 degrees F. Remove the meat from the refrigerator at least one hour before cooking.
Rub the meat all over with the salt and pepper and spread the thyme sprigs over the top. Arrange the meat on a roasting rack, fat-side up. Roast the meat 30 minutes, then reduce the temperature of the oven to 350 degrees F. Continue cooking the meat until the internal temperature at the thickest part reaches 125 degrees F, about 1 hour. Remove the meat from the oven and tent loosely with foil. (Leave the oven on.) Let rest 20 minutes.
For the horseradish cream: In a medium bowl, whisk together the sour cream, horseradish, Dijon mustard, chives and salt and pepper. Set aside.
For the sandwiches: Place the rolls on a baking sheet and brush the cut sides with some olive oil. Toast in the oven just until lightly golden, 5 to 10 minutes.
Carefully cut the meat off the bone into thin slices. Once there is enough to assemble the sandwiches, spread the horseradish cream on the rolls and layer on the meat. Serve warm.
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