Makes 6 side-dish servings
Toss zucchini with oil, salt, and pepper in a large bowl. Arrange zucchini in 1 layer in 2 shallow baking trays. Grill 1 pan of zucchini, without turning, until browned in spots and beginning to soften, 4 to 6 minutes. Drizzle 2 tablespoons balsamic vinegar over grilled zucchini and shake pan a few times, then continue to grill until most of vinegar is evaporated, about 2 minutes. Sprinkle 1/4 cup cheese over grilled zucchini and grill until cheese is melted, about 1 minute more. Repeat remaining tray of zucchini in same manner. Cool to room temperature and serve sprinkled with pine nuts.