Rib roast has more than a few common names, which often breeds confusion. Prime rib, ribeye roast, standing rib roast, Delmonico roast and rolled rib roast can all refer to the same cut, depending on how you prep it before cooking, the area of the country and, in some cases, the store you bought it from. If the term "hotel style" precedes the name of a cut of beef, especially rib roast, it usually means it was prepared with the goal of feeding a lot of people as simply as possible.
Hotel style, when referring to a rib roast, simply means boneless. Hotels commonly serve rib roasts on weekends when they have a lot of people to feed and no time for bones to get in the way of slicing, so they usually order them boneless. Depending on the hotel, you find rib roasts at a staffed carving station at the start of a buffet line, or on a rolling, heated cart taken around the dining room by a carver who slices the meat to order. The carver usually holds up one finger or two fingers together when you order, an old-school way of asking how thick you want it. A one-finger-thick slice of rib roast weighs between 8 and 10 ounces, and a two-finger-thick slice weighs between 12 and 16 ounces.
Hotel style rib roasts are a sub-primal cut, or an intermediate cut between a larger, primal cut -- in this case the rib -- and a smaller, portion cut, in this instance the ribeye steak. Hotel style rib roasts served in restaurants usually contain meat from rib No. 6 to rib No. 12 of the cow, but you sometimes find smaller rib roasts with meat from rib No. 6 to rib No. 9, or from rib No. 10 to rib No. 12, sold in grocery stores labeled "hotel style."
The U.S. Department of Agriculture grades beef according to its firmness, color, texture, physiological maturity and, most importantly, marbling. The Prime designation indicates the beef has a slightly abundant to abundant level of marbling, whereas as the Choice designation means it has slight to moderate marbling. High-end hotels and restaurants often use hotel style rib roasts from Prime beef, hence the common name, "Prime rib." In your average grocery store, however, you find Choice grade hotel style rib roasts labeled as "Prime rib." There's nothing wrong with that -- a Choice hotel style rib roast has a lot of marbling and flavor -- it just shows that Prime grade prime rib has become synonymous with the cut.
You have to cook hotel style rib roasts over low heat for one to two hours, depending on weight, and start them at a high temperature to get a sear. Season the exterior of a hotel style rib roast on all sides the night before cooking with a heavy layer of kosher salt and freshly ground black pepper. Remove the roast from the fridge a few hours before cooking to let it reach room temperature, a necessary step in cooking it evenly throughout. Sear the roast in a 500-degree-Fahrenheit oven for about 15 minutes, and then lower the heat to 300 F. Cook the rib roast until it reaches a minimum internal temperature of 120 F in the center for rare, 130 F for medium and 140 F for medium well, and pull it out of the oven. Let the rib roast rest for 30 to 45 minutes, during which time the internal temperature will rise by about 10 degrees.