Preheat oven to 350°F. Line an 8- by 8-inch pan with parchment paper with flaps so you will be able to easily lift it out of the pan after baking.
In a medium bowl, beat the eggs and tahini until smooth. Stir in coconut sugar and mix until it is thoroughly incorporated. Pour almond milk into the tahini mixture, and then add vanilla extract. Stir until combined.
In a separate bowl, whisk together almond flour, coconut flour and baking soda.
Stir the wet mixture into the dry ingredients (the batter should be thick and sticky). Fold in chocolate chips.
Transfer batter to the prepared pan and add more chocolate chips on top of the batter. Bake for 20 minutes. Cool before frosting.
In a medium bowl, combine the cocoa powder and almond butter. Add in the almond milk and stir to combine. Lastly, stir in maple syrup and mix until thoroughly combined and smooth.
When the cake has cooled, frost, slice and serve.