Remove the ribeye steaks from the refrigerator and bring to room temperature, about 20–30 minutes.
Pat steaks dry with paper towels, then rub both sides with the olive oil. Season both sides evenly with the salt and pepper.
Heat a well-seasoned cast iron skillet over medium-high heat until very hot and beginning to smoke slightly.
Add the butter to the skillet and let it melt and foam.
Place the steaks in the skillet and cook without moving for 4–5 minutes. Flip and cook the other side 4–5 minutes, or until an instant-read thermometer reaches your desired doneness (see notes for temperatures).
Transfer steaks to a cutting board and let rest for 5 minutes to allow juices to redistribute.
Slice the steaks against the grain, spoon pan juices over the slices, and serve.
Notes
Rare: 120°F.
Medium-rare: 130°F.
Medium: 135°F.
Medium-well: 140°F.
Well done: 150°F.
When melting the butter, add fresh rosemary or thyme and minced garlic to infuse more flavor.