Remove your steak from the fridge an hour before you plan to cook. This allows the interior temperature to come up a bit for more even cooking.
Preheat your oven to 350F. Rub your steaks with oil and season liberally on all sides with salt. I like to do this 30 minutes before cooking.
Heat your skillet over medium high heat until quite hot. Sear the steaks on the first side for about 5 minutes. (You should hear a good sizzle when the steaks hit the pan, otherwise it's not hot enough.) Don't move them during this time.
Flip the steaks over and add the butter, garlic, and rosemary to the pan. As the butter melts, baste the steaks repeatedly. Remember, don't move the steaks as they sear on that second side for another 4 minutes or so.
Slide the pan into the preheated oven and cook until your desired doneness. I find it very useful to insert a programmable temperature probe into the thickest part of one steak which will alert me with a beep when the meat reaches the exact temperature. The exact time will depend on how large and thick your steaks are. Mine took a full 25 minutes to reach medium rare.
Remove the steaks from the oven and set them aside on a platter to rest for 5-10 minutes. This allows the juices to redistribute throughout the meat. Top the steaks with a pat of tarragon butter, if you like.
Slice the meat against the grain and serve, with more butter if you like.
to make tarragon butter
Mash the soft butter, herbs, and garlic together with the back of a spoon until well blended.
Spoon the mixture onto a piece of plastic wrap and form into a small log. Roll up in the wrap and twist the ends tightly to secure. Chill until firm and sliceable. Alternatively you can spoon the butter into a small pot.
Notes
Prefer to grill your steak?Preheat the Grill
For gas grills: Turn all burners to high and preheat with the lid closed for 10-15 minutes.
For charcoal grills: Light the charcoal and let it burn until the coals are covered with white ash. Bank the coals to one side for indirect grilling or spread them out evenly for direct grilling.
Prepare the Steak
Take the ribeye steak(s) out of the refrigerator and let them sit at room temperature for about 1 hour.
If desired, rub the steaks with olive oil and season generously with salt and pepper. You can also add minced garlic and fresh herbs for extra flavor. Pat the seasonings onto the steak to ensure they adhere.
Grill the Steak
Place the steak(s) directly over the high heat on the grill grates.
Sear the steak on one side for 4-5 minutes until it develops a nice crust. Avoid constantly flipping the steak, as this can prevent a good sear from forming.
Flip the steak and sear the other side for another 4 minutes.
Adjust the Heat
If you're using a gas grill, reduce the heat to medium or move the steak to a cooler part of the grill. For a charcoal grill, move the steak to the indirect heat side.
Continue Cooking
Grill the steak for an additional time, adjusting the time based on your desired doneness. Use a meat thermometer to check the internal temperature:
Rare: 120-125°F (49-52°C)
Medium-rare: 130-135°F (54-57°C)
Medium: 140-145°F (60-63°C)
Medium-well: 150-155°F (66-68°C)
Well-done: 160°F (71°C) and above
Rest the Steak
Remove the steak from the grill and let it rest for about 5-10 minutes on a cutting board. This allows the juices to redistribute and results in a juicier steak.