Preheat oven to 350°F (conventional) or 325°F (convection). Grease a baking sheet and dust it with flour or line it with parchment paper.
Chop the chocolate coarsely and melt 7 oz of it in a bowl over a double boiler.
Using a hand mixer, cream together butter, sugar, vanilla extract, and salt togeter. Gradually add the eggs. Mix flour and baking powder and stir the mixture alternately with the coconut milk into the butter-sugar-egg mixture.
Pour about ⅓ of the batter in a separate bowl. Then, stir in ¾ cup of the shredded coconut.
Combine the melted chocolate and cocoa with the remaining batter.
Now, spread the chocolate batter on the baking sheet. Then add the coconut batter in blobs. Pull a fork through the batter to create a swirled pattern.
Bake for about 25 minutes, then let it thoroughly cool.
Melt the remaining chocolate together with coconut oil over a double boiler. Spread it over the cake and sprinkle with the remaining shredded coconut. Let the glaze dry before cutting the chocolate coconut cake into pieces.