Preheat oven to 350 degrees F. Coat a cooling rack with nonstick spray and place on a baking sheet; set aside.
In a shallow dish, combine Parmesan and spices and spread along bottom of dish.
Baste zucchini with olive oil and roll each spear in parmesan and spice mixture. Place zucchini onto prepared baking sheet and bake until tender, about 15 minutes. Then broil for 2-3 minutes, or until crisp and golden brown.
Serve immediately, garnished with parsley, if desired.