Preparation Slice zucchini lengthwise 1/8 inch thick with a mandoline or other hand-held slicing device. Heat a lightly oiled well seasoned cast-iron ridged grill pan over moderately high heat until hot and grill zucchini slices in batches until grill marks appear, 2 to 3 minutes on each side. Arrange zucchini slices as grilled in one layer on a platter and sprinkle with garlic and parsley. Season zucchini with salt and pepper and drizzle with oil.