Preheat oven to 350F. Grease a 9x13-inch baking pan; set aside.
In a large bowl, whisk together flour, sugar, cocoa powder, baking soda, baking powder, and salt.
Add coconut oil, yogurt, melted chocolate, eggs, vanilla, and water. Stir together until combined.
Pour batter into prepared pan.
Bake for 30-40 minutes, or until a toothpick inserted in the center comes out clean.
Let cool in pan to room temperature.
To make frosting, beat butter until smooth, about 1-2 minutes.
Add coconut milk, powdered sugar, and vanilla extract. Beat until well-combined.
Stir in pinch or two of salt, to taste.
Spread frosting over cooled cake, and top with coconut chips.
Store any leftovers covered in the fridge.
Notes
Flour: It’s important to properly measure the flour. Weighing it is the most accurate means of measurement. If not, you will need to sift the flour to avoid packing it.
Unsweetened cocoa powder: Regular unsweetened cocoa powder works well in this recipe.
Coconut oil: The coconut oil adds moisture and mild coconut flavor. If you'd like to use a different type of oil, like olive oil or vegetable oil, you can. However, I recommend adding 1/2 - 1 teaspoon coconut extract along with the vanilla extract.
Butter: I use salted butter in the frosting. The little bit of salt helps to balance out the frosting.