Rub steaks lightly with thyme, salt and pepper. Cover the steaks and set them aside on the counter, bringing them close to room temperature.
Pre-heat a gas grill on high or establish a hot bed of coals in a charcoal grill.
In a large skillet melt the butter over medium heat. Add the mushrooms and green onions to the skillet and sauté for 6 - 10 minutes until the juices from the mushrooms release. Slowly pour in the wine and cook it down until liquid is reduced by half. Add the Worcestershire sauce and remove the sauce from the heat. Set it aside while grilling the steaks.
Sear the steaks over very hot coals for 3 minutes on each side. Move the steaks to a cooler section of the grill or lower the heat and continue to cook until they are about 125 degrees in the center (medium-rare), about 5 - 6 minutes.
Move steaks to a rimmed platter and cover with foil for 5 - 7 minutes.
In the meantime, reheat the mushrooms and add any accumulated juices from the steaks to the sauce. Once the sauce is warm, whisk in one piece of butter at a time until each is completely incorporated into the sauce. Season the sauce with fresh pepper to taste.
Top each steak with sauce and a sprig of fresh thyme. Serve immediately.