1. Press coarsely cracked pepper on both sides of beef steak. Heat large nonstick skillet over medium heat until hot. Place steaks in skillet; cook 10 to 13 minutes for medium rare (145 degrees F) to medium (160 degrees F) doneness, turning occasionally. Remove to platter, season with salt, as desired. Keep warm.
2. Heat oil in same skillet over medium heat until hot. Add mushrooms and garlic; cook and stir 3 to 5 minutes or until mushrooms are tender and browned. Add beef broth, Champagne and thyme to skillet; stirring until browned bits attached to bottom of pan are dissolved. Bring to a boil; cook 4 to 8 minutes or until mixture is reduced to 1 cup. Combine cornstarch and water; stir into mushroom mixture. Bring to a boil; cook and stir 1 to 2 minutes or until sauce thickens, stirring occasionally. Season with salt, as desired.
3. Serve steaks with sauce.