Heat your grill to high flame.
Wash zucchini and trim off the ends.
Using a mandolin or vegetable peeler slice the zucchini lengthwise in thin slices.
Lightly spray with cooking spray and season with salt and pepper, to taste.
Grill the zucchini ribbons on 1 side, until lightly marked and wilted, about 1 to 2 minutes.
Remove and put on a platter and let cool slightly.
Cut up tomatoes in large chunks, season with salt and pepper to taste.
Arrange on a platter with zucchini and garnish with parsley sprigs.