Preheat oven to 350° F (175° C). Lightly spray two 9” round cake pans.
In a large bowl, whisk together the non-dairy milk, aquafaba, brown sugar and vanilla.
Shred zucchini (or other squash substitute) in a food processor or with a grater.
Stir in the shredded zucchini. I used a spiralizer to make 2 cups of zucchini, which I then quickly chopped into small pieces, and then a small food processor to make the other 2 cups. I wanted some zucchini wetter and some more dry. You could food process all the zucchini instead.
In a separate bowl, mix the whole wheat flour, cocoa powder, baking soda and salt and then add to the zucchini mixture, stirring until completely combined.
Pour evenly into the two cake pans.
Bake for 40-45 minutes or until a toothpick inserted in center comes out clean.
The cakes should rise nicely, the top might feel a bit tough, but the frosting softens it up.
Let cool completely. Run a knife around the pans and turn upside down onto a cooling rack or towel.