Begin by preparing the prime rib. If you would like to be able to make smaller slices, cut the bones off of the meat. Tie the bones back to the meat using cooking string. The bones add a lot of flavor to the meat, so you don't want to throw it away. Season all sides with salt and black pepper, making sure to pat each side before moving onto the next side so that the seasoning does not fall off. Using the tip of a knife, make make six holes into the top layer of fat. Stick a garlic clove into each hole. The garlic adds flavor to the meat as it cooks.
Remove the rosemary and thyme leaves from the stems. Set the stems aside to be used later. Mince four garlic cloves. Lay the flat side of a knife over each clove and smash it. Add the rosemary and thyme leaves to the smashed garlic cloves and chop until finely minced. Place a stick of butter into a bowl, add the garlic and herbs, and season with salt and black pepper. Mix until fully combined. This will be your butter rub.
Add a drizzle of olive oil to a sauté pan and heat over a medium/high flame. Place the prime rib on it's side to sear for about three minutes, or until a rich brown crust has formed on the surface of the meat. Searing adds a more savory flavor to the finished dish. Flip to the other side for another three minutes. Lastly, flip it onto its top side and hold the meat in place until browned. Remove from the pan and set aside to cool off.
Meanwhile, preheat the oven to 375°F with convection on, if available.
Add the celery, carrots, onion, four whole garlic cloves, and the rosemary and thyme stems to a roaster. Add a large drizzle of olive oil and season with salt and black pepper. Mix together and then place the rack on top. Cover all sides of the cooled off prime rib with a layer of the butter rub. Place the butter rubbed prime rib onto the rack, bone side down.
Cook the prime rib in the oven for forty minutes. Remove from the oven and place on the stove. Remove the rack with the prime rib and set aside. Pour the vegetables and drippings into a strainer over a bowl. Place the prime rib rack back into the roaster and back into the oven for about another hour or until the internal temperature of the prime rib roast reaches 130°F for medium. If you prefer more rare, aim for 115°F.
Meanwhile, squeeze the vegetables using a wooden spoon to release all of the remaining juice and drippings flavor into the bowl. Discard the vegetables in the strainer and set the bowl with the flavored drippings aside.
Add two tablespoons of butter to a frying pan and melt over medium heat. Slowly sprinkle in a small amount of flour into the pan. Stir until combined with the butter. You want it to have a paste like consistency. You won't need to add all of the flour. At this point, pour in the red wine. Stir until mixed together. Add one cup of water or chicken stock and stir together. You don't want it to be too liquid or too thick, so you may need to add more or less water. Reduce to a simmer and then add in the vegetable drippings from the bowl into the pan. Stir together and let simmer for about ten minutes.
Meanwhile, warm up a large drizzle of olive oil in a separate frying pan. Cook the mushrooms until tender and then add into the red gravy pan. Mix together and let cook for about another ten minutes on low heat.
Remove the prime rib from the oven once it is ready and let sit for about for about ten minutes. Remove the string and bones before slicing into it. Serve with a drizzle of the red wine mushroom gravy on top and enjoy with a side of mashed potatoes, rice or a salad. Salute and cin cin!