Preheat the oven to 350°F/180°C making sure the oven rack is in the center of the oven. Line an 8x8-inch or 20x20-cm square baking pan with parchment paper and lightly spray. Set aside.
Prep the zucchini. Wash the zucchini, slice in half lengthwise, and using a spoon, scrape out the seeds. Using the large size of of a box grater, grate all the zucchini. Gently blot them with a clean kitchen towel to remove some of the moisture. You should have about 200 grams of zucchini after squeezing.
Mix the wet ingredients. Into a large mixing bowl, add the squeezed zucchini along with the oil, plant based milk, yogurt, sugar, flax seeds, and vanilla. Mix this together until no oil is floating on top. Now add the cocoa powder to the wet ingredients. Whisk this together until the cocoa powder is fully incorporated, about 1 minute of good whisking. Adding this now ensures the chocolate is evenly distributed in the batter without over mixing the flour.
Mix the dry ingredients. Now add the flour, baking powder, baking soda, salt, and any other optional ingredients (see below). Mix this carefully, making sure to not over mix. The batter will be very thick. Pour into the prepared baking dish.
Bake. Bake the cake for 45 to 50 minutes. This cake is super thick and heavy and needs a good amount of time in the oven. You’ll know it’s done when the cake has pulled away from the edges and a toothpick inserted into the center of the cake pulls out clean. Let the cake cool for at least 30 minutes in the hot pan before removing to a wire rack to cool completely before frosting.
Make the frosting. In a large mixing bowl with a hand mixer, or in a stand mixer with a whisk attachment, cream together the softened vegan butter with 1/2 a cup of powdered sugar. Mix on high for 3 minutes to get it fluffy. Add the melted chocolate, cocoa powder, vanilla, and remaining powdered sugar. Mix on low till all is incorporated, then mix on high for 4 minutes to make the frosting nice and fluffy. Spread out over the cooled cake.
Serve and enjoy!