In a medium bowl, combine softened salted butter, minced garlic, chopped fresh rosemary, and parsley. Add Dijon mustard, Worcestershire sauce, kosher salt, and black pepper to taste. Mix thoroughly until you achieve a smooth, fragrant compound butter.

Place your bone-in prime rib roast on a clean cutting board, allowing it to rest at room temperature for at least 1 hour. Trim any excess fat if necessary and tie it with butcher twine.

Preheat your oven to a gentle 250°F (121°C). Pat the prime rib dry with paper towels, then generously rub the prepared compound butter all over the roast.

Place the prime rib on a roasting rack inside a sturdy roasting pan. Roast it for approximately 2 ½ to 3 hours, or until the internal temperature registers 100°F (38°C).

Raise the oven temperature to 400°F (204°C) and allow the prime rib to roast until it reaches an internal temperature of 125°F (52°C) for rare or 135°F (57°C) for medium.

Remove the roast from the oven and let it rest for at least 30 minutes, tented with foil.

Using the drippings from the roasting pan, carefully skim off any excess fat. Place the pan on the stovetop over medium heat, adding ⅓ cup of all-purpose flour to create a roux. Gradually add in 3 cups of beef broth, stirring until the gravy thickens.

Carve the roast into thick, juicy pieces and serve with homemade gravy drizzled over the top.