Make the thyme butter: Combine the butter and thyme in a food processor and process until smooth; season with salt and pepper. Scrape the butter into a large ramekin, cover with plastic wrap and refrigerate until cold and the flavors meld, at least 2 hours and up to 48 hours.
Make the prime rib: Remove the prime rib from the refrigerator 2 hours before roasting. Pat the surface dry with paper towels. Make 8 small slits over the surface of the fat cap with a knife and fill each slit with a whole garlic clove. Let sit at room temperature.
Fifteen minutes before roasting, place the roast on a large cutting board, brush with canola oil and season heavily with salt and pepper.
Preheat the oven to 450 degrees F. Place the roast bone-side down (fat-side up) in a large roasting pan fitted with a rack. Roast 20 minutes. Reduce the oven temperature to 350 degrees F and continue roasting until a digital instant-read thermometer inserted into the center and ends of the meat registers 120 degrees F to 125 degrees F for medium-rare doneness, about 3 hours. (Start checking the temperature after 2 hours.)
Transfer the meat to a cutting board. Pour off all but a few tablespoons of the fat from the roasting pan, then place the pan over 2 burners set to high heat. Add the shallots and the chopped garlic and cook until soft, about 4 minutes. Add the wine and a splash of vinegar and cook until reduced by three-quarters, about 5 minutes. Add the stock and peppercorns and bring to a boil. Cook until reduced by half, about 10 minutes.
Strain the sauce into a medium saucepan and set over low heat. Bring to a simmer and cook until reduced a bit further. Slowly whisk in the cold thyme butter and cook until the sauce thickens (do not boil or the sauce will break). Season with salt and pepper. Finish with another splash of vinegar. Carve the meat; serve with the sauce and garnish with parsley.