Preheat oven to 350F. LIne the bottom of an 8-inch springform pan with parchment paper (no need to butter the pan or the paper).

In a bowl, using a double boiler or microwave, melt chocolate (microwave chocolate on High for 15-second increments until melted).

Whisk in butter until melted and well combined. Set aside.

In another bowl, whisk together whole eggs, egg yolks, and 1/2 cup sugar just until combined. Slowly whisk in melted chocolate mixture. Whisk in coffee.

Using an electric mixer on medium speed, beat egg whites until foamy. Slowly add remaining 1/2 cup sugar and beat until soft peaks form. Gently fold beaten egg whites into chocolate mixture. Pour batter into the prepared pan and, using a rubber spatula, smooth top.

Bake in the preheated oven for 35 to 40 minutes, until puffed up and cracked and no longer jiggly in the center (be careful not to overbake).

Remove from the oven and let cool completely in the pan on a wire rack. (Don't worry: the cake will fall as it cools and makes a sort of crater in the center. That's for the whipped cream.)

To unmold cake, run the tip of a knife around the cake edge and then carefully remove the sides of the pan.

When ready to serve, whip cream. Fill cake crater with whipped cream. Top with coconut flakes.