Preheat oven to 350°.
Press zucchini on several layers of paper towels. Cover with additional paper towels; set aside.
Combine flour, 1 cup granulated sugar, walnuts, and next 6 ingredients (walnuts through nutmeg) in a large bowl; make a well in center of mixture. Combine milk, oil, vanilla, and eggs in a bowl; stir with a whisk. Add zucchini; stir. Add to flour mixture; stir just until moist. Divide batter evenly between 2 (8 x 4-inch) loaf pans coated with cooking spray. Sprinkle each with 1 tablespoon granulated sugar. Bake at 350° for 1 hour and 10 minutes or until a wooden pick inserted in center comes out clean. Cool 5 minutes in pans on a wire rack; remove from pans. Cool completely on wire rack.