For the cake: Preheat the oven to 325°. Beat the butter in the large bowl of an electric standing mixer until creamy. On medium speed, slowly add the sugar and beat until the sugar and butter are light and fluffy. (Stop occasionally to scrape down the sides of the bowl and beaters to ensure even mixing.) Sift together the flour, baking powder, and salt. Add the vanilla to the milk. On low speed, add the flour to the butter-sugar mixture in 3 batches, alternating with the milk. Mix only until each addition is well blended before proceeding to the next, stopping once or twice, again, to scrape the sides of the bowl and beaters.
In a separate bowl, beat the egg whites just until they form soft peaks. Stir one-third of the beaten egg whites into the cake batter to lighten, then carefully fold in the remaining egg whites. Turn the batter into three 9" buttered and floured parchment-lined cake pans, bang each cake pan gently on the counter to remove any large air pockets from the batter, and bake in the preheated oven for 20-25 minutes, until the cake centers spring back lightly when gently tapped with the fingertips. Remove immediately to cooling racks and allow to rest 5 minutes before turning out of the pans onto the racks. Cool the layers completely before peeling off the parchment bottoms.
For the filling: Stir together the egg yolks and sugar in a large nonreactive saucepan until well blended. Stir in the melted butter and cook, stirring constantly, over moderate heat until mixture thickens enough to coat the back of a spoon thickly. Take care that it does not simmer or boil. When thickened, stir in the pecans, raisins, and coconut and continue cooking for 1 minute before adding the vanilla extract and bourbon. Stir briefly over heat, then remove from the stove and allow to cool slightly before filling and frosting the cake layers.
To assemble the cake: Spread approximately 1 cup of the filling evenly between all the cake layers. Frost the top and sides of the cake with remaining filling. Allow to cool completely before cutting.