In large zipper-style plastic bag or large glass baking dish add all the ingredients for the marinade, mixing well. Place steaks into mixture and marinate for 2 hours at room temperature or for several hours in the refrigerator, turning every half hour or so.
Build a high-heat fire. Set grill rack in place, cover grill with lid and let rack heat up, about 5 minutes.
Remove steaks from marinade; discard marinade.
Grill steaks uncovered, until well browned on one side, 2 to 3 minutes. If steaks start to flame, pull them to cooler part of grill or extinguish flames with a spray bottle filled with water.
Once steaks are well browned on both sides, slide each one to cooler part of grill. Continue grilling over medium fire to desired doneness, 5 to 6 minutes more for rare (120° F), 6 to 7 minutes for medium rare (125° F), 7 to 8 minutes for medium rare (130° F) or 8 to 9 minutes for medium (135*-140° F). Let steaks rest 5 minutes and then serve immediately with Mushroom Sauce spooned atop the steaks.
In a small bowl whisk together the lemon juice, Worcestershire sauce, soy sauce, Tabasco and basil leaves. Set aside.
Melt the butter in a large sauté pan over medium-high heat. Add the mushrooms, onions and garlic and sauté for 2 minutes, stirring occasionally. Add reserved mixture and simmer, uncovered for about 5 minutes, stirring occasionally. Season to taste with salt and pepper.
Servings: 4