Heat large nonstick skillet over medium heat until hot. Add Ground Beef; cook 8 to 10 minutes, breaking into 3/4-inch crumbles and stirring occasionally. Remove from skillet with slotted spoon; season with 1/2 teaspoon salt and 1/4 teaspoon pepper. Set aside. Pour off drippings from skillet.
Heat oil in same skillet over medium heat until hot. Add mushrooms and onion; cook 3 to 4 minutes or until vegetables are tender, stirring frequently. Return beef to skillet. Add thyme; cook 3 to 5 minutes or until heated through, stirring frequently. Remove from heat. Set aside.
Whisk milk, eggs, remaining 1/2 teaspoon salt and 1/4 teaspoon pepper in large bowl until blended.
Spray 2-1/2 to 3-quart shallow baking dish with nonstick cooking spray. Layer half of the bread cubes, 1/2 cup of the cheese and half of the beef mixture in dish. Pour half of the egg mixture over the top. Top with remaining bread cubes, 1/2 cup of the cheese and remaining beef and egg mixtures. Sprinkle with remaining 1 cup cheese. Press any dry bread cubes into egg mixture. Cover with aluminum foil; refrigerate 6 hours or as long as overnight.
Preheat oven to 350°F. Bake strata, covered, 55 minutes. Remove foil. Bake, uncovered, 10 to 15 minutes or until puffed and lightly browned. Let stand 5 minutes. Top with tomatoes and basil, as desired.
Nutrition information per serving: 450 Calories; 198 kcal Calories from fat; 22 g Total Fat; 10 g Saturated Fat; 0 g Trans Fat; 1.6 g Polyunsaturated Fat; 5 g Monounsaturated Fat; 210 mg Cholesterol; 870 mg Sodium; 26 g Total Carbohydrate; 2 g Dietary Fiber; 36 g Protein; 4 mg Iron; 443 mg Potassium; 3.2 mg Niacin; 0.4 mg Vitamin B6; 2.4 mcg Vitamin B12; 5.6 mg Zinc; 34.4 mcg Selenium; 171.1 mg Choline;