How to Make It
Preheat the oven to 350°. Spray an 11-by-17-inch jelly-roll pan with vegetable oil spray and line the bottom with parchment paper; spray the paper.
In a small saucepan, bring the cream to a boil. Remove from the heat, add the chocolates and let stand for 5 minutes, then whisk until smooth. Pour 1 cup of the chocolate ganache into a measuring cup and set aside at room temperature; scrape the rest into a bowl. Cover the bowl with plastic wrap and refrigerate the ganache until firm, at least 3 hours.
In a medium saucepan, bring 1 inch of water to a bare simmer. Using an electric mixer, beat the eggs and sugar in a large bowl at medium speed until blended. Set the bowl over the simmering water and whisk until the eggs are warm to the touch. Remove from the heat and beat at high speed until tripled in volume, about 5 minutes. Fold in 3 2/3 cups of the coconut. Spread the batter in the prepared pan in an even layer. Bake for about 25 minutes, or until golden and firm. Let the cake cool for 15 minutes.
Run a knife around the edge of the cake; invert it onto a baking sheet and peel off the parchment. Slide the cake onto a work surface. Using a serrated knife, trim the edges and cut the cake into 3 rectangles of equal size. Stack the layers and trim off any uneven sides with the knife.
Set 1 cake layer right side up on a wire rack and spread with half of the chilled ganache. Cover with a second layer and the remaining chilled ganache. Top with the third cake layer, smooth side up; press down gently. Pour half of the reserved ganache on top and spread it evenly, letting it drip slightly down the sides. Pour on the remaining ganache and smooth the top and sides. Transfer the cake to a cake plate. Refrigerate for 15 minutes, then press the remaining coconut onto the sides of the cake. Garnish with chocolate curls and serve or, for best results, refrigerate the cake overnight.