In a shallow glass dish or bowl, stir together the soy sauce, Italian dressing, cornstarch, garlic and ginger. Place steak strips in the mixture to marinate for 15 minutes.
While the beef is marinating, combine the bouillon cubes in water in a large saucepan. Bring to a boil, and add pasta. Cook for about 8 minutes, or until al dente. Drain.
Heat a large skillet over medium-high heat. Remove beef from marinade with a slotted spoon, and place in the hot skillet. Discard marinade. Cook beef, stirring constantly for 2 to 3 minutes, or until mostly browned. Stir in the beef broth, mushrooms and green onions, reduce heat to medium-low, cover, and simmer for about 5 minutes. Remove lid, add broccoli, and cook until broccoli is bright green and tender but still crisp. Add drained linguine, toss, and serve.