Pat steak dry with paper towels and sprinkle with salt and pepper. Heat oil in 12-inch skillet over medium-high heat until just smoking. Place steak in skillet and cook for 30 seconds. Flip steak and continue to cook for 30 seconds. Continue flipping steak every 30 seconds for 3 more minutes.

Slide steak to back of skillet, opposite handle, and add butter to front of skillet. Once butter has melted and begun to foam, add shallot, garlic, and thyme sprigs. Holding skillet handle, tilt skillet so butter pools near base of handle. Use metal spoon to continuously spoon butter and aromatics over steak, concentrating on areas where crust is less browned. Baste steak, flipping it every 30 seconds, until steak registers 120 to 125 degrees (for medium-rare), 1 to 2 minutes.

Remove skillet from heat and transfer steak to cutting board; tent with aluminum foil and let rest for 10 minutes. Discard aromatics from pan and transfer butter mixture to small bowl. Slice steak thin and serve with butter mixture.