How to Make It
Preheat the oven to 350°. Lightly butter two 8-by-2-inch round cake pans and line the bottom of each pan with wax paper. Lightly butter and flour the wax paper.
In a food processor, pulse the pecans with 1/4 cup of the sugar until very finely ground; transfer to a medium bowl. Sift together the flour and baking powder and add to the nuts. Whisk to blend.
Combine the eggs and the remaining 3/4 cup sugar in the large bowl of a standing electric mixer. Set the bowl over a saucepan of simmering water; do not let the bowl touch the water. Whisk the eggs and sugar until warm and the sugar is dissolved, about 4 minutes. Remove from the heat and beat at medium high speed until cool, pale and tripled in volume, 5 to 8 minutes.
Sprinkle about 1/2 cup of the dry ingredients at a time over the eggs, gently folding in each addition with a rubber spatula. Drizzle the melted butter down the side of the bowl in 2 additions and gently fold in.
Scrape the batter into the prepared pans and smooth the top. Bake in the bottom third of the oven for 25 to 30 minutes, or until the center springs back when touched and the edges are golden. Let the cakes cool in the pans for 20 minutes. Then run a knife around the cakes and invert onto racks to cool completely.
In a medium heatproof bowl, whisk together the sugar, cornstarch and salt. Whisk in the whole egg and egg yolk until smooth. In a saucepan, bring the coconut milk and heavy cream just to a boil over moderate heat. Gradually whisk the hot liquid into the egg mixture. Pour the pastry cream into the saucepan and cook over moderate heat, stirring, until very thick and close to a boil, about 5 minutes. Remove from the heat and stir in the butter and vanilla, then add the coconut. Let cool briefly, whisking occasionally. Press a piece of wax paper directly on the surface and refrigerate until chilled, at least 3 hours or overnight.
Using a large serrated knife, split each of the cakes into 2 layers. Invert the top layer of one cake onto a cake platter and spread 1/2 cup of the coconut pastry cream on top. Invert the bottom layer on top of the first layer and peel off the wax paper. Spread another 1/2 cup of pastry cream on top. Continue with the remaining cake layers and pastry cream. Cover the cake with plastic wrap and refrigerate.
In a small bowl set over a pan of barely simmering water, melt the chocolate, butter and corn syrup, stirring occasionally. Remove from the heat and set aside until cool to the touch.
Slowly pour the glaze onto the top of the cake and, using a small metal icing spatula, spread it evenly over the surface. Spread it just to the edge, or let a little drip down the sides of the cake. To serve, slice the cake gently with a serrated cake knife.