Since this is now a Christmas Roast thread ....

I bought a USDA Prime Grade Prime Rib from Costco -- 5.58 lbs and boneless.
I assaulted it with sea salt and pepper, and let it sit uncovered in the fridge overnight.
Next morning, took it out to assume room temp before cooking. Warming it up to room temp can take a couple hours or more.
In the bottom of the roasting pan, I placed LARGE CHUNKS of sweet onion, celery, mushrooms. garlic and carrots. Also added fresh thyme, red wine (Merlot), and beef stock. I then rubbed the outside of the roast with a mixture of Extra Virgin Olive Oil (don't skimp on those virgins!), butter, minced fresh garlic, Kosher salt and more fresh ground black pepper and thyme. I thought about tying the roast with some twine, but it was already pretty uniform in shape. I'll try that next time to see if there's a difference.
The roast was placed on top of the veggie "rack" in the roasting pan and placed in a preheated oven at 250°F.
I chose the
Reverse Sear method from all the methods I researched. I've done that with steaks before. Once the meat is cooked evenly throughout (not so much "gray" around the edges, but medium rare from crust to crust), then you sear if after it rests.
Anyway, I bought a temperature probe set from Amazon that works well. I set one probe for 117° to give me a little heads- up to get ready, and the other at 120° -- the temp at which I wanted to remove the roast.
When the roast was at 120°, I put it on the counter and draped a sheet of foil over it loosely. I let it rest for about an hour (recommended to rest 45-90 minutes) to allow the juices to seep throughout the meat. Actually, I wound up having to let it go beyond that, because the oven was being used for other things. But, that's fine.
The last step was to remove the probes and foil, and heat the oven to 500° -- or however high yours can go. Once it was hot, I place the roast on a wire rack in another pan, and let it sear for 10 minutes. 15 minutes is the max you should allow it to sear, but 10 minutes at 500° was perfect to create that crispy crust.
While the roast rested, I made the au jus from the drippings and liquid in the bottom of the roasting pan. I scoop out the veggie remains, sifted the juice through a strainer, and let it sit until the fat rose to the top. I used a large freezer ziploc to hold the liquid and put it in the fridge for a few minutes. The fat rose and congealed. I snipped one corner of the bag, and drained the de-fatted liquid into a bowl. I put the fat in a skillet with some flour. Cooked and stirred that for 3 minutes, then gradually added back the juice a little at a time, bringing it to a boil, then adding more juice. Cook that for about 10 minutes after all the juice is added. It'll reduce the wine and blend all the flavors.
I also made some horseradish sauce from sour cream, horseradish (duh), and small parts vinegar, Worchestershire, brown mustard and fresh chives. I did that the day before. You need to let it sit in the fridge for about an hour after making anyway, so I did it way ahead to get it out of the way.
Once the roast is seared, it's ready to carve. Let it cool for a minute, so you aren't touching a 500° piece of meat! No need to let it rest -- that was done before the searing. The only part of the roast actually cooked in the final step is the outer crust.
During resting, I left the probes connected to the thermometer. Both probes about 4 inches apart rose to exactly 136°F while resting outside the oven -- from a temp of 120° when removed. That's exactly what I was shooting for. It's just on border between medium-rare and medium -- as requested by my daughter. Medium-rare is 130°-135° in most charts I've seen.
Doing the reverse sear worked great. There is the seared crust, then about 1/8th inch of medium, and the entire inside was an even medium-rare.
My son-in-law and daughter both said the crust was outstanding with lots of delicious but not overwhelming flavors.
And my SIL also said the au jus was better than any he's had in restaurants.
The number one thing I think is important is the temperature probes. Time estimates are okay, but for a cut of meat this expensive, it's better to know exactly when the temperature reaches the cutoff. Overcooking would be a major disappointment.
Having said all of that about reverse sear, if you're feeding people who are wanting a range of medium-rare to medium-well, then regular searing at the start might be the better method, so there's some "more cooked" meat at the edges.
Because this was my first Prime Rib, I wanted to do a good job. I watched SO MANY videos. That's how I learned to reverse sear steaks -- by cooking them on the stove top at low temp, then searing them in the oven on high temp. A cast iron skillet is a must-have.