Heat large nonstick skillet over medium heat until hot. Place beef Ribeye Steaks in skillet; cook steaks 12 to 15 minutes for medium rare (145°F) to medium (160°F) doneness, turning occasionally. 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.
Season steaks with salt and pepper, as desired. Serve sauce with steaks.
Nutrition information per serving: 493 Calories; 198 kcal Calories from fat; 22 g Total Fat; 11 g Saturated Fat; 7 g Monounsaturated Fat; 138 mg Cholesterol; 409 mg Sodium; 21 g Total Carbohydrate; 0.9 g Dietary Fiber; 45 g Protein; 4.5 mg Iron; 16.6 mg NE Niacin; 1 mg Vitamin B6; 2.4 mcg Vitamin B12; 9.1 mg Zinc; 79.9 mcg Selenium; 28 mg Choline;