Bring the steak to room temperature, about 20 minutes.
Season the steak with salt and pepper. Heat a large, heavy skillet over medium high heat. When the pan is very hot, add the oil then add the steak and sear, without moving the steak, for 5 minutes until nicely browned on the bottom. Use tongs to flip the steak, and then add the butter to the top of the steak. Place the herb sprigs next to the steak in the pan. Cook the meat for about another 4 to 5 minutes without moving the steak, allowing the butter to melt, and using a spoon to baste the top of the meat with the seasoned butter. For medium rare the middle of the steak should be 130 F on a meat thermometer.
Remove the steak to a cutting board with a moat to catch the juices. Let the steak rest for 5 to 10 minutes before slicing.
While the meat is resting, return the pan to medium heat and add the garlic. Sauté for 30 seconds then remove the pan from the heat.
Slice the steak across the grain. Arrange the slices on a plate and spoon the pan sauces in the skillet over the slices. Sprinkle with additional salt and freshly ground pepper.
Notes
You should plan on about 6 ounces of rib-eye per person, more of course if you know you have devout steak lovers. And whenever you make a steak, plan for leftovers! A salad with sliced steak is a lunchtime treat, or you can use the meat, or of course a sandwich on a crusty baguette with spicy mayo.A rib-eye steak often weighs about 20-ounces or more, and one steak will feed 2, 3 or more people. Once the steak is nicely sliced and plated on a serving platter or individual plates people it will feel like a generous portion of meat.