Preheat the oven to 350℉ and line a 8 X 8 baking pan with parchment paper.
In a large bowl, using a hand held mixer, whisk together the warm coconut oil, coconut sugar and vanilla for 30 seconds, then add in the eggs and whisk for another 15 seconds until smooth.
In a separate bowl, add the buckwheat flour, cocoa powder, almond flour, baking soda, salt and stir until well combined.
Add the dry ingredients into the wet ingredients and whisk on low setting until smooth and starts to look like a brownie batter. Fold in the zucchini and chocolate chunks.
Transfer the batter to the prepared baking pan and smooth over with the back of the spatula. Bake for 18 to 20 minutes and allow to cool completely in the pan on a wire rack.
While the brownie is baking, prepare the chocolate avocado frosting. In a food processor, add the coconut icing sugar, cocoa powder, coconut oil, vanilla and avocado. Process for 30 seconds or until smooth and well blended.
Spread the frosting on top of the cooled brownie and slice into squares. Store any leftovers in an airtight container at room temperature for up to 2 days, or in the freezer for up to 1 month.