Heat 2 teaspoons oil in a large cast-iron skillet over medium-high heat. Sprinkle steak with salt and 1 teaspoon black pepper. Add one-third of steak to pan; cook 45 seconds on each side. Remove from pan; keep warm. Repeat procedure with remaining steak.
Add remaining 2 teaspoons oil to pan. Add white onion, celery, bell pepper, and garlic; sauté 3 minutes or until vegetables are tender. Sprinkle flour over vegetables, and stir well to combine. Add the diced tomatoes, tomato sauce, and olives; stir well to combine. Add broth; stir until well blended. Add remaining 1 teaspoon black pepper, basil, thyme, and hot pepper sauce.
Return steak to pan; bring to a boil. Reduce heat, and simmer 1 hour or until steak is tender. Stir in green onions and parsley. Serve over grits.