Preheat an indoor or outdoor grill to medium-high. Place the zucchini in a bowl and toss with 2 Tbsp. of the oil, salt, and pepper. Grill 1 to 2 minutes per side, and then arrange on a large platter. Top with the basil leaves.
Drizzle the zucchini with the remaining olive oil and the balsamic vinegar. Sprinkle with the pine nuts and cheese and serve.
Note: To toast the pine nuts, place in a single layer in a small baking dish. Bake, shaking the dish from time to time, in a preheated 300 degrees F oven for 10 to 15 minutes, or until lightly toasted. A vegetable peeler is a good tool to use to shave Parmesan cheese into thin pieces.