Sprinkle steak evenly with salt and pepper.
Heat a large nonstick skillet over medium heat for 2 minutes. Melt 1/2 teaspoon butter with 1/2 teaspoon oil. Add steak, and cook until well browned on one side, about 6 minutes. Turn steak, and cook 3 more minutes (rare), 4 minutes (medium-rare), or 5 minutes (medium). Remove steak from pan, and set aside.
Melt remaining 1/2 teaspoon butter with 1/2 teaspoon oil in skillet over medium heat. Sauté mushrooms and garlic 4 minutes. Stir in wine, broth, and balsamic vinegar, stirring to loosen particles from bottom of skillet. Bring to a boil; reduce heat, and cook 4 to 5 minutes.
Toss together spinach, tomatoes, onion, and hot mixture in pan; divide evenly between 4 plates. Squeeze lemon, drizzling juice evenly over top.
Cut steak into 1/2-inch slices, and arrange over salads. Sprinkle cheese evenly over top.