Pat steaks dry with a paper towel. Season generously with salt and pepper.

Heat oil in a skillet over high heat. Place steaks in the hot skillet and immediately turn down the heat to medium-high. Cook for 4 minutes. Turn steaks, add 1 tablespoon butter and thyme sprigs to the pan, and cook for an additional 4 to 6 minutes. Remove steaks from skillet and let rest for 5 minutes.

Meanwhile, make pan sauce: remove skillet from heat. Quickly saute the garlic for 1 to 2 minutes in the skillet using residual heat. Return the skillet to medium-low heat and add beef broth. Bring to a boil and reduce for 3 minutes.