Preheat oven to 400ºF. Warm a 12-inch skillet over high heat until very hot. Pat steak dry; sprinkle generously with salt and pepper. Add oil to skillet and swirl to coat. Brown steak on both sides, turning once,1 to 2 minutes per side. Transfer skillet to oven and roast for 7 to 8 minutes for medium-rare. Place meat on a cutting board; cover loosely with foil.
Set same skillet over medium heat; add 2 Tbsp. butter to juices in pan. When butter has melted, add onions and sauté until very soft, 10 to 12 minutes. Pour in wine, stir in thyme and raise heat to high. Cook, scraping up browned bits from bottom of skillet with a wooden spoon, until wine has almost boiled away and sauce is syrupy, 2 minutes. Stir in juices from cutting board. Remove skillet from heat, swirl in remaining butter, and season sauce with salt and pepper. Thinly slice steak across the grain, transfer to a platter and spoon onion mixture over meat.