Preheat the oven to 350 degrees. Coat a 9 x 13-inch baking dish with coconut oil.
Make the cake by combining the flour, sugar, cocoa powder, baking soda, and fine salt in a large bowl.
Whisk together the coconut oil, coffee, and vanilla in a separate bowl until well combined.
Add the coconut mixture to the flour mixture, then add the well-beaten eggs and milk. Mix using a rubber spatula until combined; the batter will be thin.
Pour the batter into the prepared baking dish.
Evenly sprinkle the mini chocolate chips over the top.
Bake the cake by placing the baking dish in the oven for 30-35 minutes, or until a wooden skewer inserted in the center comes out clean.
Remove from the oven to cool on a wire cooling rack for 30-45 minutes.
Make the frosting when the cake has cooled by beating the melted butter, powdered sugar, cocoa powder, warm milk, and vanilla in a large bowl with a hand mixer until creamy and smooth. Add more milk as needed until the frosting becomes thicker but still drizzly, about 1 minute. Taste and add more sugar if desired.
Frost the cake by immediately spreading the frosting over the cake. Let the frosting set for 1 hour before topping with chocolate shavings, if desired. Slice and enjoy.
Store covered at room temperature for up to five days.