1. Prepare your grill.
2. Make a basting sauce by combining the broth, olive oil, garlic powder, oregano, and thyme in a small bowl. Set aside.
3. Trim away any excess fat from the steaks, and sprinkle both sides with black pepper and salt, if desired. Grill filet mignon steaks for 3-5 minutes on each side depending on desired degree of doneness. Transfer the cooked steaks to a warm plate, cover, and set aside.
4. Place the onion slices and mushrooms in a shallow grilling pan, and brush with some of the basting sauce. Grill for about 5 minute on each side. Cook, turning and basting occasionally, for about 10 minutes, or until the mushrooms are tender and the onions are soft and browned.
5. Meanwhile brush the inside of each roll half with some of the basting sauce and lightly toast on the top rack of your grill or away from direct heat so the bread doesn't burn. Place the halves cut side up on individual plates.
6. Thinly slice each steak and arrange the slices over 1 roll. Repeat with the other steaks and rolls.
7. Toss the mushrooms and onions with the remaining basting sauce. Spoon over the steak, letting any excess fall over the sides onto the plate. Serve immediately.
Nutrition information per sandwich: 480 calories, 14 grams fat, 41 grams carbohydrates.