How to Make It
Preheat oven to 450°.
Combine oil, vinegar, thyme, 3/8 teaspoon salt, 3/8 teaspoon pepper, and sugar in a large mixing bowl. Add mushrooms, garlic, and shallots; toss. Using a slotted spoon, place vegetables on a foil-lined jelly-roll pan coated with cooking spray. Reserve vinegar mixture. Bake vegetables at 450° for 25 minutes or until tender, stirring twice. Remove from pan. Cool slightly. Coarsely chop mushrooms and shallots. Remove skins from garlic. Add vegetables, garlic, and any accumulated liquid to vinegar mixture.
Heat a grill pan over medium-high heat. Sprinkle steak with remaining 1/4 teaspoon salt and remaining 1/2 teaspoon pepper. Add steak to pan; grill 5 minutes on each side or until desired degree of doneness. Remove from pan; let stand 10 minutes.
Trim all fat from steak, including eyes of fat in center. Discard fat. Cut meat into very thin slices. Add lettuce to mushroom mixture; toss gently to coat. Divide mushroom mixture evenly among 4 plates. Top evenly with sliced steak and blue cheese.