Take your roast out of the fridge at least an hour before you plan to cook it, to take the chill off. Preheat your oven to 500F (or as high as it will go).
Prep the roast by rubbing it all over with soft butter, then sprinkling with thyme, salt and pepper. Set a heavy cast iron skillet over medium-high heat for a minute or two to warm it up; put the roast into the pan and slide it into the oven. Multiply the weight of the roast by 5, and roast it for exactly that many minutes - for example, a 4 lb roast x 5 = 20 minutes. After that time, turn the oven off and leave it inside for 2 hours.
When you take the roast out, set it on a cutting board and put the skillet back on the stovetop. Sprinkle over about a tablespoon of flour - more if you’re making a large roast - and whisk over medium-high heat until it bubbles and thickens. Whisk in about 1/2 cup of stock or water and a splash of wine (if you like), bring it back to a simmer and stir until it has the consistency you want, adding a little more stock or water if it’s too thick. If it’s too thin, simmer it on the stovetop until it reduces.
Slice and serve the prime rib with the gravy. Serves about 3 per pound.