Coat a small nonstick skillet with cooking spray. Place over medium-high heat until hot. Add mushrooms, green onions, and salt; saute 8 minutes. Remove mushroom mixture from skillet, and set aside.
Sprinkle both sides of each steak with pepper. Coat skillet with cooking spray; place over high heat until hot. Add steaks, and cook 1 1/2 to 2 minutes on each side or until lightly browned. Remove steaks from skillet; drain and pat dry with paper towels. Set aside.
Place 1 sheet of phyllo on a damp towel (keeping remaining phyllo covered). Lightly coat phyllo with cooking spray. Top with another sheet of phyllo, and coat with cooking spray; fold in half crosswise, bringing short ends together. Place 1 steak 3 inches from one end of phyllo. Spoon half of mushroom mixture over steak. Fold short end of phyllo over mushroom mixture; fold lengthwise edges of phyllo over steak, and roll up, jellyroll fashion. Repeat procedure with remaining 2 sheets of phyllo, mushroom mixture, and steak.
Lightly coat phyllo packets with cooking spray; place, seam side down, on a baking sheet coated with cooking spray. Bake at 425° for 15 to 17 minutes or until golden. Serve immediately.