Discard the outermost slices of zucchini and brush the rest of the slices with the oil on both sides. Season with salt and pepper. Place on a preheated grill or grill pan for about 4 minutes on each side, or until tender.
In a small bowl combine the goat cheese, parsley leaves and lemon juice, mashing with a fork.
Put 1/2 teaspoon of the cheese mixture about 1/2-inch from the end of a zucchini slice. Top with a few spinach leaves and 1 small, or half of a large basil leaf. Roll up and place seam side down on a platter. Repeat with the rest of the zucchini slices.