Dry-brine the roast. Pat the prime rib very dry with paper towels. Season generously with kosher salt on all sides. Place the roast on a wire rack set over a rimmed baking sheet and refrigerate uncovered for at least 12 hours (or up to 48 hours) to dry-brine.

Bring to room temperature. Remove the roast from the refrigerator about 3 to 4 hours before cooking to ensure it cooks evenly throughout. Preheat the oven to 250°F (121°C).

Make the garlic-herb butter. In a small bowl, stir together the softened butter, rosemary, thyme, garlic, black pepper, onion powder, Dijon mustard, and smoked paprika until evenly combined.

Assemble the roasting pan. Scatter the onion, carrot, celery, and smashed garlic in the bottom of a large roasting pan. Pour in the beef stock or water. Set a roasting rack over the vegetables, place the roast on the rack (fat-cap side up), and spread the garlic-herb butter evenly all over the meat. Season the roast generously with extra freshly-ground black pepper.

Slow-roast. Transfer to the oven and roast until the internal temperature reaches 120°F for medium-rare or 125°F for medium, about 3 to 3½ hours, depending on your oven and roast size.

Rest. Remove from the oven, tent loosely with foil, and let rest for 20–30 minutes to allow the juices to redistribute.

Make the au jus (while the roast rests). Spoon or pour off most of the fat from the roasting pan, leaving just 2 to 3 tablespoons along with any browned bits. Place the pan over medium heat, add the wine, and simmer for 2–3 minutes, scraping up all of the caramelized drippings. Stir in the beef stock, thyme (or rosemary), and bay leaf, then simmer gently for about 10 minutes to let the flavors meld. → Tip: If your roasting pan isn’t stovetop-safe, transfer the browned bits and drippings to a saucepan and prepare the au jus there instead. → Optional thickening: Whisk together the cornstarch and cold water in a small bowl to form a slurry. Stir the slurry into the simmering au jus and cook for 1–2 minutes, until slightly thickened. Strain through a fine-mesh sieve, then season with salt and pepper to taste.

Sear. Heat a large cast-iron skillet over high heat with a tablespoon of a high heat oil (such as avocado oil) or beef tallow. Carefully transfer the rested roast to the hot skillet and sear on all sides for 1–2 minutes per side, until a rich, golden-brown crust forms.

Slice and serve. Remove the rib bones, slice the roast against the grain into ½-inch-thick slices, drizzle with warm au jus, and sprinkle with flaky sea salt just before serving.