Preheat oven to 350°F.

Grease a 9" springform pan with butter and dust with coconut sugar, tapping out any excess.

Combine chocolate, oil, and butter pieces in a large heatproof bowl. Place the bowl over a saucepan of simmering water and melt, stirring often. Remove bowl from saucepan and set aside.

Add the yolks to a medium bowl and add cocoa powder, vanilla, salt, 1/4 cup sugar, and remaining 2 whole eggs and whisk until mixture is smooth. Slowly whisk yolk mixture into chocolate mixture and combine well.

Using an electric mixer on high speed, beat egg whites until frothy. With mixer running, gradually add remaining 1/2 cup sugar; beat until firm peaks form.

Gently fold egg whites into chocolate mixture in 2 additions, folding just until incorporated between additions. Scrape batter into prepared pan; smooth top and sprinkle with remaining 2 tablespoons sugar.

Bake the cake until the top is puffed and cracked and the center is no longer mushy, about 40 minutes. Be careful not to overbake the cake.

Cool the cake in the pan on a wire rack. The center of the cake will sink as it cools, forming a sort of crater.

When ready to serve, whip the cream with the confectioners’ sugar and vanilla until not quite stiff. Using a spatula, carefully fill the sunken center of the cake with the whipped cream, spreading decoratively. Sprinkle the top lightly with cocoa powder and chocolate shavings, if desired. Run the tip of a knife around the edge of the cake, carefully remove the side of the pan, and serve.