Preheat broiler. Place steak on the rack of an unheated broiler pan. Broil 3 inches from heat for 15 to 17 minutes or until medium doneness (160℉), turning once halfway through broiling. Cool slightly; cut into thin slices. Place steak slices in a resealable plastic bag set in a shallow dish; set aside.
For marinade, in a screw-top jar, combine oil, vinegar, mustard, and oregano. Cover and shake well. Pour marinade over steak slices. Seal bag; turn to coat steak slices. Marinate in the refrigerator for at least 6 hours or up to 24 hours, turning bag occasionally.
Drain steak slices, discarding marinade. To serve, arrange shredded lettuce in a chilled large bowl. Place steak slices, tomatoes, avocado, cheese, bacon, and eggs on top of the lettuce. Drizzle some of the Dijon Vinaigrette over salad. Pass remaining Dijon Vinaigrette.
To make dijon vinaigrette
In a small bowl, combine white balsamic vinegar, mustard, garlic, sugar, salt, and pepper. Add olive oil in a slow steady stream, whisking constantly. Makes about ⅔ cup.