Preheat your oven to 450°F (230°C). In a small bowl, mix together olive oil, smoked paprika, garlic powder, onion powder, black pepper, salt, and cayenne pepper (if using). Rub the spice mixture all over the prime rib, ensuring an even coating. Let it sit at room temperature for about 30 minutes.

In a large skillet over medium-high heat, sear the prime rib on all sides until browned (about 2-3 minutes per side). This step enhances the flavor and creates a nice crust.

Place the prime rib in a roasting pan and insert a meat thermometer into the thickest part of the meat. Roast in the preheated oven for 20 minutes, then lower the temperature to 325°F (165°C). Continue roasting until the internal temperature reaches your desired doneness (130°F for medium-rare, 140°F for medium). Once done, remove from the oven and let it rest for at least 20 minutes before slicing.

In a separate pan, melt butter over medium heat. Add the chopped leeks and cook until softened, about 5 minutes. Add the chopped mushrooms to the leeks and cook until they release their moisture and become golden brown, about 7-10 minutes.

Sprinkle flour over the mushroom and leek mixture, stirring to combine. Cook for an additional 2 minutes to eliminate the raw flour taste. Gradually whisk in the beef broth, Worcestershire sauce, and soy sauce, bringing the mixture to a simmer. Cook until thickened, about 5-7 minutes. Season with salt and pepper to taste.

Slice the prime rib and serve with the rich smoked mushroom gravy drizzled on top. Garnish with fresh thyme sprigs.