In a small bowl, empty the can of cream of chicken soup, undiluted, into a small bowl. Stir in the nutmeg. Add the 2 Tbs. milk, and stir to blend with soup. Put in refrigerator.
In a medium bowl, combine baking mix, Parmesan cheese, and egg, until mixed together well and crumbly. Put in refrigerator.
Wash zucchini; do not peel. Slice zucchini into 1/4 in. thick slices. Cook in microwave, until mostly cooked. Take out and let cool, until you are able to handle.
Preheat oven to 350 degrees. Spray a 9 x 13 in. baking dish with cooking spray or grease.
Put all of the zucchini on bottom of baking dish. Top with cut-up chicken. Get soup mixture and baking mix/egg mixture out of refrigerator. Spread soup mixture over chicken. Sprinkle the baking mix/egg mixture over the soup mixture.
Sprinkle with dried parsley. Melt light butter, and drizzle over the top.
Bake in preheated oven for 25-30 minutes, until golden brown.