Stir together oil and vinegar in a shallow baking dish. Add zucchini and toss to coat. Season with salt and pepper.
Allow zucchini to marinate while you heat the grill over medium-high heat (5-600°F).
Carefully spray the grill or brush with olive oil. Arrange the zucchini on the grill.
Cook for 2 minutes per side (lid down), then an additional 2-6 minutes (depending on the size of your zucchini and the heat on your grill). Zucchini should be soft but not mushy.
Turn the grill to low, then carefully sprinkle tops of zucchini rounds with parmesan. Put the barbecue lid down and cook for one more minute.
Carefully remove zucchini from the grill.
Serve with extra balsamic vinegar or balsamic reduction.
Notes
Nutritional info excludes balsamic reduction as this is an optional topping.