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Rib-eye steaks, also called Delmonicos, are among the most flavorful cuts of beef, so they deserve special care when cooking. They're a favorite for grilling season, but you can fry a rib-eye in a skillet indoors and still develop a desirable crust on the outside. A medium-well steak is well browned throughout most of the steak but has a bit of pink in the center. For best results, choose a rib-eye that's at least 1 inch thick so the center doesn't cook through before the outside develops a crust.
Season the rib-eye about 45 minutes before you plan to cook it. While you can use any seasoning for the steak, basic salt and pepper are most typical.
Line the bottom of a skillet with oil and preheat it over medium heat for about 10 minutes or just until the oil begins to smoke. Use a cast iron skillet if possible; cast iron heats evenly and holds heat.
Place the rib-eye in the oil carefully, moving quickly to avoid any oil splatter as the steak hits the hot oil.
Turn the steak, and use tongs so you don't pierce the meat. Some cooks prefer to flip a steak only once after developing a crust on the first side, but you can turn the steak as often as once every minute to cook it evenly and keep both sides evenly hot. Spoon the hot oil over the up-facing side to encourage browning and to baste the meat.
Remove the rib-eye from the skillet when the internal temperature reaches 145 degrees Fahrenheit. Insert a digital thermometer in the thickest part of the steak to read the temperature.
Rest the steak on a plate for at least three minutes to allow the juices to redistribute throughout the meat, as well as to allow the internal temperature to rise to 150 F, the temperature guideline for a medium-well steak.
Although it isn't necessary, you might wish to add some butter to the pan for the last few minutes of cooking to help flavor the meat. You can also add aromatic herbs and onions or shallots.