“The” way to prepare a tasty (and expensive) ribeye roast -- from my mom's aunt. Works for her and works for me on the rare treat that we buy a ribeye roast. The roasts I use are usually 4-6 lbs, but here's an instance where size doesn't matter.
I love this recipe because I can prepare it with great ease and convenience, all the while making the best tasting roast ever. For a dinner party, I may start the roast at 2 pm, then with all my extra time put effort into other dishes -- like twice-baked potatoes, salad, and dessert. I have a double oven, so I can prepare my other sides without the forbidden opening of the oven door.
If you went to the great expense to buy a ribeye roast, make your roast this way. No butter -- no flour -- no garlic -- certainly no basting. Just follow the simple instructions. I think it's best at medium-rare -- that's pink in the middle but warm. You may use a meat thermometer if you like, but I've never needed to when following the instructions.
If you have the "convection" setting on your oven, don't use it. Just use the conventional setting. If you must use the convection setting, you'll need to use a meat thermometer or adjust cooking times as convection will cook the meat faster. I learned the hard way -- conventional oven does a perfect job using the following instructions while convection will make it more medium-done.