Place zucchini on several layers of paper towels; cover with additional paper towels. Let stand 10 minutes, pressing down occasionally.
Weigh or lightly spoon flour into dry measuring cups; level with a knife. Combine flour, 6 tablespoons cocoa, and next 3 ingredients (through 1/4 teaspoon salt) in a medium bowl, stirring with a whisk.
Place granulated sugar and next 4 ingredients (through vanilla) in a large bowl; beat with a mixer at medium speed until lemon-colored (about 5 minutes). Add eggs, 1 at a time, beating well after each addition. Add flour mixture to sugar mixture; beat at low speed 1 minute or just until combined. Add zucchini and chocolate chips; beat at low speed 1 minute or just until combined. Spoon batter into a 9 x 5-inch metal loaf pan coated with baking spray. Bake at 350° for 38 minutes or until a wooden pick inserted in center comes out clean. Cool in pan 10 minutes on a wire rack. Loosen edges from sides using a narrow spatula. Remove from pan, and cool completely on wire rack.
Combine powdered sugar, remaining 1 tablespoon cocoa, milk, and dash of salt in a small bowl, stirring until smooth. Drizzle over loaf.
BAKE A SECOND BATCH If you have two loaf pans available, then double the mix. Cool and wrap baked cakes whole and unglazed in plastic wrap. To ship overnight, pack securely in a box, or gather a pretty cloth around the cake to hand-deliver. The icing is wet; pour it into a zip-top bag and include instructions to snip the corner and drizzle onto the cake.
Didn't use the glaze and accidentally used cornstarch instead of baking powder! Despite that goof, the eggs and soda helped the loaf rise nicely. It's not oversweet, and we found it perfect for lunchboxes and afternoon snack, as well as a dessert if you add some vanilla or chocolate ice cream. It also makes incredible ice cream sandwiches. Might not be to everyone's taste as it does have a pronounced cocoa flavor (which I like but not everyone does) and it's not gooey sweet, but we enjoyed it.
Made this for a family dinner last night and everyone just loved it. The loaf was easy to make and came out moist, tender, and not overly sweet. I followed the recipe exactly except for using dark chocolate chips instead of semi-sweet and half-and-half for the icing instead of milk. Watch your baking time, though -- mine had to stay in for 12 minutes longer than the recipe specified to ensure that the center was done. All in all, it was a great way to use up some seasonal zucchini and I would definitely make it again.