Preheat oven to 350 degrees.
In a sifter, or large bowl, add sugars, flour, cocoa, salt, and soda. If using a bowl, stir together. Set aside.
Grate zucchini and set aside.
In a mixing bowl, mix eggs, buttermilk, and vanilla.
Add dry ingredients and begin mixing on low speed. Slowly pour melted butter into batter while mixing.
Add zucchini and stir, by hand, to combine. You don't want to mix too much after addition of zucchini or it will wring the zucchini out and make it too watery.
Pour into a greased jelly roll pan.
Bake for 20-22 minutes.
ICING:
While cake is baking make icing.
In a saucepan, melt butter over low heat. Add cocoa powder and stir until nice and smooth.
Add milk and vanilla, stir.
Add powdered sugar and salt. Stir until it is smooth.
Add chopped walnuts if desired, or reserve to sprinkle on top after cake is iced.
As soon as you remove cake from the oven, pour warm icing evenly over cake . Let it set for a few minutes, if you can!