Allow the steak to rest at room temperature, covered, for 30 minutes prior to cooking.

Heat a sauté pan over medium-high heat and add the oil. Season the steaks with salt and pepper to taste on both sides.

Sear in the hot pan until deeply caramelized, 3 to 4 minutes. Flip the steaks over and repeat.

Reduce the heat to low, and add the butter and thyme sprigs. Using a large spoon, baste the steaks with the butter. Continue to cook until the steak is done to your liking. An internal temperature of 125° and 130° is ideal for medium rare.

Transfer the steaks to a dinner plate, and top with a spoonful of Sauce Verte.