Pound steak to 1/4-inch thickness with a meat mallet or rolling pin. Cut steak into 2-inch squares; set aside.
Combine flour and next 4 ingredients in a large heavy-duty, zip-top plastic bag. Add steak; seal bag, and shake to coat.
Brown half of steak in 1 tablespoon butter in a Dutch oven over medium-high heat about 2 minutes on each side. Remove from Dutch oven; keep warm. Repeat procedure with 1 tablespoon butter and remaining steak. Remove from Dutch oven.
Add remaining 1 tablespoon butter, onion, and next 3 ingredients to Dutch oven. Cook over medium heat, stirring constantly, 5 minutes or until vegetables are tender. Add tomatoes and water; return steak to Dutch oven. Cover, reduce heat, and simmer 45 minutes, stirring once.
Spoon grillades over grits, and serve hot.