Combine balsamic vinegar, low-sodium soy sauce, olive oil, Worcestershire sauce, honey, Italian seasoning, and dried mustard in a gallon-size zipper bag or a large bowl.

Add the steaks to the marinade. Seal the bag or cover the bowl, ensuring the steaks are fully coated. Marinate for at least 20 minutes or up to 8 hours for maximum flavor.

Preheat your grill to medium-high heat, approximately 350-400 degrees Fahrenheit.

Remove the steaks from the marinade and discard the marinade. Place the steaks on the hot grill for 4-5 minutes per side for a 1-inch steak, aiming for medium-rare.

Use an instant-read thermometer to verify doneness. For medium-rare, aim for 130°F; for medium, 140°F; and 150°F for medium-well. Let steaks rest for 5-10 minutes before serving.

Sprinkle with coarse kosher salt or sea salt flakes, and garnish with fresh parsley if desired.