Preheat broiler. Slash fat edges of steak at 1-inch intervals, being careful not to cut into the meat. 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 degree F), 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. Makes 6 servings.
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 2/3 cup.