Preheat your oven to 180C/350F, and line a 20cm/8inch cake pan with parchment paper.
In a large bowl, whisk together flour, cornstarch, cocoa, baking powder, baking soda, and salt.
In a separate bowl, combine soy milk, apple cider vinegar, peanut butter, syrup, vegetable oil, apple puree, flax egg, and shredded zucchini, whisking until well blended.
Mix the liquid ingredients into the dry ingredients until a smooth batter forms.
Pour the batter into the prepared cake pan and bake for 50 minutes. Test for doneness using a toothpick, and allow the cake to cool completely.
While the cake cools, make a quick frosting by blending the listed ingredients until smooth. Transfer the frosting to a piping bag and refrigerate for an hour before assembling.
Cut the cake in half and spread ⅓ of the frosting on the bottom half. Add more frosting on top and use a spatula to create a smooth surface. Optionally, decorate with chocolate chips.