Heat 3 teaspoons of the oil in a large skillet over medium-high heat until hot. Cook onions and 1/2 teaspoon of the salt for 4 minutes or until slightly softened, stirring once.
Add all remaining ingredients except steak and remaining oil and salt; cook 3 minutes or until water has evaporated. Reduce heat to medium, cook 15 minutes or until onions are tender, stirring frequently. (Onions can be made up to 3 days ahead. Cover and refrigerate.).
Meanwhile, heat grill. Brush both sides of steak with remaining 1 teaspoon oil; sprinkle with remaining salt. Grill, covered, over medium heat or coals 8 to 10 minutes for medium-rare to medium, turning once. Serve topped with warm onions.