For Onions: In a large skillet, cook the onions in butter or margarine over medium-low heat, covered, for 13 to 15 minutes or until onions are tender. Uncover skillet and increase heat to medium. Continue cooking, turning frequently, until onions are golden.
Meanwhile, For Steaks: In a small bowl, blend together Worcestershire sauce, garlic, parsley, basil, salt, and pepper. Rub over both sides of steaks.
Brush a griddle or an extra-large heavy skillet with some cooking oil. Heat over medium-high heat until hot. Add steaks; reduce heat to medium and cook for 5 to 8 minutes, turning steaks occasionally, or until desired doneness.
If you like, spread the cut sides of the kaiser rolls with steak sauce or a mustard blend. Serve the steaks on kaiser rolls; heat with caramelized onions.