Place the grated zucchini in the middle of a kitchen towel. Twist the ends together and squeeze the juices out of the vegetable. In a large skillet over medium-high heat, heat the 1 tablespoon of the oil with garlic. Saute the zucchini, dill and salt and pepper until tender but still crisp. Toss the zucchini with remaining oil and check seasoning. Top with parsley.