Set ribeye out at room temperature for 1 hour
Generously sprinkle with salt and pepper. Don't forget the sides, too.
Turn on stove to a medium-medium high heat, place skillet on top, let pan get nice and hot before placing steak in it. This will help give it a fantastic sear which is called a Maillard² reaction. See more about that in the notes section below. Place steak in, laying it away from you. It's good practice to do this any time.
Let the steak sear for about 3-4 minutes. Don't flip it. Just let it cook and check to make sure it's not burning. You want a crust, not burnt.
Pick the steak up in your tongs and hold it on its side until the fat is rendered. Not only does the steak look nicer, but rendered fat makes any steak taste better. Flip the steak to the opposite side until you achieve one of two things. 1.Your desired internal temperature (explained below) using a meat thermometer. Place it directly in the center of the thickest part. OR2.A very nice crust on both sides. If you have and your steak is not done to your desired temperature, then you can use your oven (preheated to 400°F) to finish the cook. *If your steak is grey, then you haven't achieved the right look... or taste. Try until you reach the desired temperature When your steak has reached the desired temperature, turn off the stove.
Toss the butter, garlic, and rosemary into the skillet.
Take your spoon, tilt your skillet safely toward you, and begin basting your steak for about 1 minute.
Place your steak on a clean plate and tent (upside down V) foil it for 20 minutes. This will complete the cooking for you as well as allowing the steak to reabsorb the juices.
Enjoy that juicy, oh-so-tasty, why have you been paying so much at restaurants all this time, steak. This will turn you into a steak snob and that's PERFECTLY acceptable.