Whisk together soup and next 3 ingredients until smooth; set aside.
Sprinkle 1 teaspoon salt and 1 teaspoon pepper evenly over steaks. Stir together remaining 1/2 teaspoon salt, 1/2 teaspoon pepper, and flour in a shallow dish. Dredge steaks in flour mixture.
Fry steaks in hot oil in a large skillet over medium-high heat 2 minutes on each side. Remove steaks, reserving drippings in skillet. Add mushrooms and thyme, and sauté 3 to 4 minutes or until lightly browned.
Stir reserved soup mixture into mushroom mixture in skillet; cook 1 minute, stirring to loosen particles from bottom of skillet. Bring to a boil, and return steaks to skillet. Cover, reduce heat, and simmer 15 to 20 minutes or until done.