Preheat grill to medium-high heat. Combine oil, oregano, garlic powder, salt and pepper in a small bowl.
Make crosswise cuts every ½ inch along each zucchini, slicing almost to the bottom but not all the way through. Gently fan the zucchini to open the cuts wider and place a small piece of Parmesan into each cut. Brush the oil mixture over the top.
Place the zucchini on a double layer of foil and grill, without turning, until browned and tender, 16 to 18 minutes.