Preheat the oven to 180 C (350 F). Grease a 8x8 inch baking pan and line with parchment paper.
In a large bowl, mix together eggs, vanilla, coconut sugar, and yogurt or applesauce until well combined. Let the mixture sit for 5 minutes so coconut sugar dissolves.
In a separate bowl mix together flour and cocoa powder (sift the cocoa powder if it is lumpy), baking soda and salt until well combined and no lumps remain.
Add the dry ingredients to the wet and mix until just combined, then fold in zucchini and chocolate chips.
Spread the batter into the prepared pan, sprinkle extra chocolate chips on top, then bake 20-25 minutes. A toothpick should come out with sticky crumbs on it but not totally wet goo. If you over bake, these will be cakey.