Heat large nonstick skillet over medium heat until hot. Place steaks in skillet; cook 3/4-inch thick steaks 8 to 10 minutes (1-inch thick steaks 12 to 15 minutes) for medium rare to medium doneness, turning once. Remove steaks; keep warm. Season with salt and pepper, as desired.
Add mushrooms and thyme to same skillet; cook and stir 3 to 5 minutes or until tender. Remove mushrooms; set aside.
Add balsamic vinegar to skillet; increase heat to medium-high. Cook and stir 7 to 10 minutes or until browned bits attached to skillet are dissolved and sauce is reduced to 1/4 cup.
Stir in butter, mushrooms and 1/4 teaspoon salt. Cook and stir until heated through. Serve sauce with steaks.