Ready in 45 minutes
* Whisk all ingredients in small bowl to blend.
* Season dressing to taste with salt and pepper. (Can be prepared 1 day in advance. Cover and refrigerate.)
* Whisk first six ingredients to blend in a 13x9x2-inch baking dish.
* Add steaks to marinade, turn to coat. Cover & refrigerate for at least 8 hours.
* Combine onions, lemon juice and salt in medium bowl. Let stand for one hour, tossing occasionally.
* Prepare grill. Remove steaks from marinade. Sprinkle with salt & pepper.
* Grill 3 minutes per side for medium rare. Transfer steaks to work surface.
* Melt butter if skillet over medium-high heat. Add shallot and mushrooms; saute until well browned, about 7 minutes.
* Add vinegar to skillet and bring to a boil, scraping up browned bits.
* Remove from heat and mix in oil. Season mixture with salt & pepper.
* Combine lettuces, onions, and mushroom mixture in bowl. Toss.
* Divide lettuce mixture among 6 plates. Thinly slice steaks across grain; arrange atop lettuce mixture.
* Drizzle some of Aioli over salads. Pass remaining Aioli separately.
Preparation Time: Marinate steak 8 hours in advance. Prep till serve takes about 35 minutes.