Heat toaster-oven broiler (or oven broiler), with rack set 4 inches from heat. Season steak with salt and pepper; place on a broiler-proof pan. Broil 4 to 6 minutes, without turning, for medium-rare. Let rest 5 minutes.
Meanwhile, in a medium bowl, combine oil and vinegar; season with salt and pepper, and whisk to combine. Add spinach; toss to combine. Thinly slice steak crosswise. Place spinach, grapes, and steak on a serving plate. Sprinkle with cheese and walnuts.