Pat the prime rib completely dry. Rub evenly with kosher salt and black pepper, covering the fat cap and bones. Place uncovered on a wire rack over a baking sheet and refrigerate for 24–48 hours.
In a large pot, heat olive oil and brown the beef bones on all sides for 10–12 minutes. Add onion, carrots, celery, and garlic. Stir in tomato paste and cook for 1 minute. Deglaze with red wine, scraping the pot. Add beef stock, beef base, thyme, and bay leaf. Simmer uncovered for about 3 hours to reduce and deepen flavor.
Remove roast from the fridge and let sit uncovered at room temperature for 5–6 hours before roasting for even cooking.
Preheat oven to 250°F (120°C). Place the roast on a rack in a roasting pan. Insert a meat thermometer into the center and roast for approximately 3 hours, or until internal temperature reaches 120°F for medium-rare.
Remove from oven, tent loosely with foil, and let rest 20–30 minutes. This allows juices to redistribute and temperature to rise to about 130°F.
Increase oven temperature to 500°F (260°C). Return roast to oven and sear for 1–2 minutes per side, until deep brown and crisp.
In a bowl, combine sour cream, horseradish, Dijon mustard, Worcestershire, and mayonnaise. Stir until smooth and refrigerate until serving.
Strain the simmered broth, discard solids, and skim off excess fat. Season with salt and pepper. Serve warm alongside the sliced roast.
Carve against the grain into thick slices and serve with warm Au Jus and cold horseradish sauce.