Preheat oven to 350 degrees Fahrenheit. Grease a 9×13-inch baking pan.

In a small saucepan over low heat, melt eight ounces baking chocolate with the oil. Stir until combined. Remove from heat and let cool.

In the bowl of an electric mixer fitted with the whisk attachment, beat whites. When foamy, slowly add in one-third of a cup sugar and beat until stiff peaks form. Remove whites from bowl and set aside.

In the bowl of an electric mixer, combine yolks with remaining sugar. Beat on high speed until light and creamy, about three minutes. Using a spatula, incorporate the nuts, then the egg whites. Fold in cooled chocolate.

Set aside one cup of batter (refrigerate it). Pour cake into prepared pan. Bake for 50 minutes.

Spread shredded coconut on a cookie sheet and toast until just golden, about five minutes.

Once cake has cooled, melt remaining two ounces baking chocolate. Stir into the reserved cup of batter. Spread mixture over cake to glaze. Top with shredded coconut.

Keep cake refrigerated.