Preheat oven to 375 degrees. Grease and flour or spray well with baking spray a half sheet pan (13 by 18 inches).
Melt chocolate over low heat in a small heavy-bottomed saucepan or double boiler. Let cool slightly.
In a large bowl whisk together well the sugar and eggs.
Once chocolate has cooled some, gradually whisk it into the egg/sugar mixture.
Whisk in vegetable oil, applesauce, and vanilla extract.
Combine both flours, baking powder, baking soda, and salt. Add to bowl and stir until incorporated.
Stir in zucchini and chocolate chips.
Pour batter evenly into prepared pan, using a spatula to spread it evenly into the corners.
Bake for 25 minutes or until firm to the touch in the middle.
To make icing, use an electric mixer to beat butter until fluffy. Add cocoa powder and evaporated milk and beat on low speed until blended. Gradually add powdered sugar. Spread icing on cake. (It is easiest to do this if the cake is still a little warm.)