Preheat the BBQ to medium-high, and lightly oil the plate or grill.
Cut the zucchini in half crosswise, then slice each half into 3 slices lengthwise, making 6 slices per zucchini.
Mix the butter, garlic, and parsley in a bowl, and spread the mixture on both sides of each zucchini slice. Sprinkle one side of each slice with Parmesan cheese, and place the slices, cheese sides up on the BBQ.
Cook the zucchini until the cheese has melted and the slices are cooked through, about 8 minutes.