A prime-cut steak like this only needs to be handled so that it stays juicy and tender and not overcooked. Salt/Pepper or rubs that you find in the recipe section works well. Heat should only be high to sear both sides for no more than 2 minutes per side, after which the heat needs to be lowered to cook the center without overcooking the surface. On a stove top, this is best done with an oven safe pan to sear on both sides, then into a preheated 400 degree (F) oven until done. On a grill, this is high direct flame heat for searing only, then move the steaks over to a section of the grill with no direct flame and use the lid and grill thermometer to manage like the oven instructions just mentioned. Watch that the grill does not overheat beyond 400 degrees, which is very common if you just put the lid on and walk away.
This cut should be cooked using an internal meat thermometer that is oven safe, no matter the method of cooking. These devices cost $20 and are critical for the best eating experience and are as useful a tool as a spatula. The internal Fahrenheit temperature goals are: 115-120 Extra-Rare (Bleu); 120-125 Rare; 125-130 Medium Rare; 130-135 Medium. Not recommended to go above 135 degrees.
The Rib Eye Steak cut is very flavorful and tender due to the fact that it comes from the upper rib cage. The muscles in the upper rib cage do not support the animal’s weight, nor does it have to work hard like the leg muscles. These steaks are cut to 1.25 inches thick.