Thanks Kayb!

@innoabrd. Yes! That is in my opinion the only way to cook rib roasts or any large piece piece of meat. I have always (after searing) cooked rib roast at the desired finished temp. And in my experience the last rib roast of the night that had been held at 140F for at least four hours was always the best and juiciest. Not sure if there is any fact in that just an observation.

ChefDaddy, that's an excellent explanation. Thank you for it; I'm copying and pasting for my files.

We used to cook prime ribs slow at my late-step father's restaurant (The Library in Denver, for you old-timers). The theory was that why cook them at a higher temperature than you wanted them to end up? So we'd cook them rare, around 130 or 140 as I recall, literally overnight!

Well, Eye of round roast is what I am going to assume you're talking about. Any way you try you have a large piece of meat. And the best way so far that you cook a large piece of meat such as eye of round roast or standing rib roast or even whole beef tenderloin is to go slow so that you don't over cook the meat. French culinary technique would say to season, sear and cook to desired temp. But being that it is a roast it has to cook slow (not briasing) so that you end up with the desired temp (med. rare). The faster you cook it the more you will have well done from the outside in. If you were to cook at 350F until the center reaches 135-145F in the center you have a small area of med rare and the rest will be medium all the way to well done at the outside edge. In short you would have shades of doneness. But, If you cook it at say 250F or even 150F you will have minimal shade of doness by the time the center reaches medium rare. So, I would treat it like a standing rib roast.
Season, sear at 500F reduce temp to 150F or so and let it go until it reaches desired temp.
This takes a long time and if you decide to shorten the time a bit and cook at a higher temp then be careful of carry over cooking which occurs when something is removed from heat but continues to cook a little more. Which can take your roast from meduim rare to medium in about five minutes of standing once out of the oven. So if you cook your roast at a higher temp then pull it out 5-10 degrees sooner than the desired temp.

The Cook's Ilustrated method is the one most raved about, and that's likely the one you mean. The meat is presalted the day before. Then the roast is seared off for flavor. Then it's cooked at 225F until it reaches 115F. Then it sits in a turned off oven for about another 20 minutes to 125F for rare/medium rare.

I have used this method to make this cut, only leaving it at 225 for the entire time. It came out fairly tender. When I've used higher heat, the roast can be tough. Still with this method it is a very lean cut, I've never seen it offered in a restaurant. You will want to slice it very thinly. Use an electric knife or a commercial slicer if you have access.