Preheat the oven to 350°F (175°C). Grease and flour a 9×13 inch sheet pan.
In a large bowl, sift together the flour, sugar, cocoa powder, baking soda, baking powder, and salt.
In a separate bowl, whisk together the vegetable oil, eggs, and vanilla extract until well combined.
Add the wet ingredients to the dry ingredients and mix until just combined.
Stir in the grated zucchini and chopped walnuts (if using).
Slowly add the boiling water to the batter, mixing gently until smooth. The batter will be thin.
Pour the batter evenly into the prepared sheet pan.
Bake for 30 to 35 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and allow it to cool completely in the pan on a wire rack.
While the cake is cooling, prepare the frosting: In a medium bowl, beat the softened butter and cocoa powder together until smooth.
Gradually add the powdered sugar alternately with milk, beating to spreading consistency.
Stir in the vanilla extract.
Spread the frosting evenly over the cooled cake.
Cut into 12 squares and serve.