Trim fat from steak. Score steak on both sides by making shallow cuts a 1-inch intervals in a diamond pattern. Place steak in a resealable plastic bag set in a shallow dish.
In a small bowl, combine French dressing, Italian dressing, and soy sauce. Pour over steak; seal bag. Marinate in the refrigerator for 2 to 24 hours, turning bag occasionally.
Prepare Bordelaise Sauce; keep warm while cooking steak
Remove steak from refrigerator; drain and discard marinade. For a charcoal grill, grill steak on the rack of an uncovered grill directly over medium coals for 17 to 21 minutes for medium (160 degree F), turning once. (For a gas grill, preheat the grill on high heat for 10 to 15 minutes. Reduce heat to medium. Place steak on grill rack over heat. Cover and grill as above.) (For broiler, place the meat on the unheated rack of a broiler pan. Broil 3 to 4 inches from the heat for 15 to 18 minutes for medium (160 degree F), turning once.)
To serve, thinly slice steak diagonally across the grain. Transfer to serving platter and cover with Bordelaise Sauce.
In a medium saucepan, heat olive oil over medium heat. Add mushroom caps. Cook and stir 2 minutes. Add garlic. Cook and stir 1 minute. Carefully add dry red wine. Bring just to boiling; reduce heat. Simmer, uncovered, for 5 minutes or till reduced to about 2 tablespoons liquid. Add beef broth. Bring to just boiling; reduce heat. Simmer, uncovered, about 10 minutes or till desired consistency, stirring occasionally. Makes about 1-1/2 cups sauce.