Preheat your oven to 350 degrees and line 3 9-inch cake pans with parchment paper on the bottom, rubbing the sides generously with coconut oil.
Place the avocado and coconut milk into a food processor (I used a small, 3-cup one) and blend until VERY smooth. Place into a large bowl.
Add in the coconut sugar, egg yolks (make sure the whites are in a separate bowl) and vanilla and beat, using an electric hand mixer, until well combined.
In a separate bowl, whisk together the coconut flour, tapioca starch, cocoa powder, baking soda and salt. Add it into the wet ingredients and blend on low speed until combined. Fold in the chopped chocolate.
Clean the beaters off VERY well and beat the egg whites until they form stiff peaks, about 5-6 minutes. Fold them into the batter a little bit at a time, very gently. You want no white streaks to remain.
Divide the batter evenly between the prepared pans and bake until a toothpick inserted in the center comes out clean, about 25-30 minutes. Let cool COMPLETELY before frosting.