1. Pat steaks dry with paper towels and season with salt and pepper.
2. Heat 2 teaspoons oil in large skillet over medium-high heat until just smoking. Cook steaks until well browned, 3 to 5 minutes per side. Transfer to plate and tent with foil. Pour off fat but do not wipe out pan.
3. Meanwhile, whisk vinegar, shallot, mustard, and remaining oil in bowl. Season with salt and pepper.
4. Return skillet to medium-high heat. Add mushrooms and 3 tablespoons vinaigrette and cook until mushrooms are golden, 6 to 8 minutes. Set aside and allow mushrooms to cool for 5 minutes.
5. Toss spinach, capers, mushrooms, and remaining vinaigrette in large serving bowl. Slice steak thinly and arrange over salad. Sprinkle with blue cheese. Serve.