Total time: 1 1/2 hours, plus overnight standing
Servings: 24 pieces
Note: Unsweetened shredded coconut is available at health food stores. If you don't have superfine sugar, put a scant cupful of regular sugar in a food processor, grind, then measure out 1 cup.
1 1/2cups cake flour, sifted
2 teaspoons baking powder
6 egg yolks, room temperature
1 cup superfine sugar
1/3 cup boiling water
3 tablespoons unsalted butter, divided
2 teaspoons vanilla extract
1 pound powdered sugar
1/3cup unsweetened cocoa powder
1/3 cup milk
Dash kosher or sea salt
2 cups unsweetened shredded coconut
1. Heat the oven to 350 degrees. Butter a 13-by-9-inch baking pan.
2. Sift the flour, baking powder and salt together and set aside.
3. In the bowl of an electric mixer on high speed, beat the egg yolks until thick and lemon-yellow, about 10 minutes. Gradually beat in the superfine sugar and beat 2 to 3 minutes longer. Melt 1 tablespoon of the butter in the boiling water. Add the vanilla and slowly beat the butter mixture into the egg mixture. Sift the flour mixture over the batter and carefully but thoroughly fold it in so that no white spots remain. Pour the batter into the prepared pan and spread evenly.
4. Bake until the cake springs back when touched gently in the center, 25 to 30 minutes. Cool in the pan on a rack for 2 to 3 hours, then cover loosely with foil and let stand overnight (the cake will crumble if cut too soon).
5. Sift the powdered sugar and cocoa into the top of a double boiler or stainless steel bowl set over, but not touching, simmering water. Add the remaining butter and the milk and whisk until smooth. Add a dash of salt and continue whisking until the coating loses its raw, sweet edge, about 5 minutes. Turn off the heat, but keep the pan over the water while cutting the cake so that the frosting does not harden.
6. Run a sharp knife around the edges of the cake pan to loosen, then cut the cake into 24 pieces and lift each out with a spatula. Using a serrated knife, carefully slice any outside edges (top, sides) off each piece. Place the coconut in a large shallow bowl. Have ready a large wire rack set over a baking sheet to catch any chocolate drippings.
7. Using a long-handled, two-pronged fork, carefully dunk each piece into the hot chocolate to coat completely, on all sides. Let the excess drip off and immediately dredge in coconut, turning carefully to coat all sides. Transfer to a rack to cool and let the coating set, about half an hour.