Preheat the oven to 350 degrees. Grease and flour a baking pan, and set aside.
In a bowl, whisk together the almond flour, coconut sugar, tapioca flour, and baking powder. Add the egg yolks, coconut milk, coconut oil, vanilla extract, and apple cider vinegar, and beat for about four minutes or until incorporated.
In a separate bowl, beat the egg whites until stiff peaks form. Incorporate the egg whites to the batter in three additions using a spatula.
Transfer the batter to the prepared cake pan, and put in the oven.
Bake for 45 to 60 minutes or until done.