Season the steak generously with salt and pepper. Place in a large food storage bag and add ½ cup dressing. Let marinate at room temperature for 10 – 30 minutes (or refrigerate for up to 8 hours). Remove the steak from the marinade and discard the marinade.
Heat a grill or grill pan to medium-high heat. Cook the steak 5 minutes per side. Let sit for 10 minutes.
Toss the mozzarella cheese, tomatoes, red onion slices and parsley with ¼ cup dressing. Arrange on a platter. Slice the steak and lay on top of the salad. Drizzle the steak with the remaining ¼ cup dressing.