Pat the ribeye steaks dry with paper towels. Season both sides evenly with kosher salt and freshly ground black pepper.
Heat a large cast-iron skillet over medium-high heat until very hot, about 3 minutes.
Add the olive oil to the skillet and swirl to coat the bottom.
Place the steaks in the skillet and cook without moving for 4 minutes to develop a brown crust.
Flip the steaks and cook for another 3 minutes for medium-rare, or longer to your desired doneness.
Reduce the heat to medium and add the minced garlic, unsalted butter, and fresh thyme leaves to the skillet.
Tilt the skillet slightly and use a spoon to baste the steaks with the melted garlic butter for 1-2 minutes.
Remove the steaks from the skillet and let them rest on a cutting board for 5 minutes before slicing and serving.