Prep Work: Combine first 5 ingredients to marinate meat. (steps #1-2) Wash, dry and chop arugula and/or romaine.
Mix oil, juice, oregano, garlic and Worcestershire in shallow dish.
Salt and pepper steak on both sides. Pierce all over with tip of sharp knife front and back. Lay in marinade and turn over to coat. Cover dish and refrigerate 4 hours or longer, or at least an hour in a pinch.
Heat broiler to high and position rack so that meat will be 6" from broiler (usually the second rung). Place steak on greased broiler pan and broil for 5-6 min. on each side. ( Internal temperature read with a meat thermometer should be approx. 145-150 degrees for medium , or 130-140 for medium rare. ) Move to cutting board and rest under a "tent" for 10 min. Slice thin strips for topping dishes.
While steak is broiling, combine second listings of olive oil and lime juice with balsamic vinegar in small bowl. Whisk in 1/4 tsp. each pepper and salt, and then 1/2 tsp. sugar or honey. Taste, then add more salt or sweetener as desired.
Toss greens with dressing, top with shaved carrots, meat and sprinkle parmesan over all. Photo above shows whole grain bread, organic butter and marmalade on the side.
(inspired by Renegade Lunch Lady Chef Ann Cooper in her book Lunch Lessons: Changing the Way We Feed Our Children)