Directions

1. Make the cake Position a rack in the center of the oven and heat the oven to 325°F. Coat a 13×18-inch rimmed baking sheet with cooking spray. Put the chocolate and cocoa in a medium heatproof bowl, add the boiling water, and whisk to combine and melt the chocolate. Set aside to cool slightly. In a small bowl, combine the flour, baking soda, and salt. Beat the sugar and butter in a stand mixer fitted with the paddle attachment on medium speed until light and fluffy, 3 to 5 minutes, stopping to scrape the bowl halfway through. Add the eggs one at a time, beating well after each addition. Slowly add the buttermilk and vanilla—the batter will look curdled at this point. Reduce the mixer speed to low. Alternate adding the flour mixture (in 3 additions) with the chocolate mixture (in 2 additions), ending with the flour mixture. Scrape the batter into the prepared pan and tap the pan on the counter to level the batter. Bake until the cake springs back when poked in the center with a finger, about 20 minutes. Cool completely in the pan on a wire rack. (Well-wrapped, the cake will keep for up to 2 days in the refrigerator, or up to 1 month in the freezer.)
2. Make the coconut-pecan filling Pulse the coconut and pecans in a food processor until they resemble coarse cornmeal. Combine the sugar, butter, egg yolks, evaporated milk, and vanilla in a 3-quart saucepan. Cook over medium-low heat, stirring constantly with a spoon or spatula, until the mixture is thick enough to coat the spoon and hold a trail when a finger is drawn through it, 6 to 7 minutes. Transfer to a stand mixer fitted with the whisk attachment and whip on high speed until cooled, fluffy, and slightly lightened in color, 6 to 10 minutes. Add the coconut-pecan mixture and beat on medium speed until combined, 1 minute more. Refrigerate until ready to use. (You can refrigerate the filling for up to 1 week.)
3. Make the chocolate mousse Melt the chocolate and butter in a large bowl set in a skillet of barely simmering water. Remove from the heat and stir with a spatula to combine. Set aside to cool slightly. Whip the egg whites in a clean stand mixer fitted with a clean whisk attachment on medium-high speed to soft peaks, 1 to 2 minutes. Slowly add the sugar and continue to whip to stiff peaks, 3 to 4 minutes. In a medium bowl, whip the cream with a whisk or electric hand mixer to medium-stiff peaks. In a small bowl, combine the egg yolks, vanilla, and salt. Mix the egg yolk mixture into the chocolate mixture with a spatula. Fold in the whipped egg whites, then fold in the whipped cream—there shouldn’t be any visible streaks.
4. Assemble the bombes Set two silicone bombe molds that hold at least 5 bombes each (3-1/4-inch diameter and 1/2-cup capacity) on a 13×18-inch rimmed baking sheet. Turn the cake out onto a cutting board. Use a 3-1/8-inch round cutter to cut 10 circles from the chocolate cake. Reserve the remaining cake for another use. Scoop about 1/4 cup of the mousse into each mold and smear it evenly all over the insides of the molds with the back of a small spoon. Refrigerate or freeze until set, 10 to 20 minutes. Evenly distribute the coconut-pecan filling among the molds (about 2-1/2 Tbs. each), and then gently press a cake circle into each mold. Cover with plastic wrap and freeze overnight. Unmold the frozen bombes one at a time onto a wire rack set in a rimmed baking sheet. Let sit until nearly room temperature, 2 to 3 hours.
5. Glaze the bombes Put the chopped chocolate and corn syrup in a medium stainless-steel bowl. In a small saucepan, heat the cream over medium-high heat until just boiling, then pour it over the chocolate mixture and let sit for 3 minutes. Whisk gently until smooth. Transfer to a liquid measuring cup for easy pouring. Pour the glaze evenly over the bombes to coat them completely. Refrigerate until set, about 2 hours. (Glaze the bombes no more than 8 hours in advance.) Let the bombes sit at room temperature for about 30 minutes before serving.