Heat grill to medium-high heat. Season the steak with 1/2 teaspoon salt and 1/2 teaspoon pepper. Grill to the desired doneness, 4 to 5 minutes per side for medium-rare. Transfer to a cutting board and let rest 5 minutes before slicing.
Meanwhile, brush both sides of the eggplant and peppers with 3 tablespoons of the oil. Season with 1/2 teaspoon salt and 1/4 teaspoon pepper. Grill until tender, 4 to 5 minutes per side.
In a small bowl, combine the remaining oil, vinegar, garlic, and parsley. Divide the steak and vegetables among individual plates. Spoon the sauce over the vegetables or serve on the side.
Tip: To serve this meal to a crowd, double the recipe and make it several hours in advance. Refrigerate, then serve at room temperature. You can use leftovers in sandwiches.