Heat the oven to 350°F (175°C), with a rack in the middle. Lightly butter two 9-inch round cake pans at least 3 inches deep and line the bottoms with parchment. Do not substitute shallow pans.

Beat the softened cream cheese with the filling sugar until smooth. Add the filling egg and vanilla; mix on low just until combined, scraping the bowl. Cover and refrigerate while making the cake batter.

Place the chopped white chocolate in a dry heatproof bowl over a saucepan of barely simmering water; keep the bowl above the water. Stir until melted, then remove from the heat and let cool until lukewarm but still fluid.

Whisk the flour, baking soda, and salt in a separate bowl.

Beat the softened cake butter and cake sugar until lighter and fluffy, about 3 to 4 minutes. Beat in the cake eggs one at a time, scraping the bowl between additions. Mix in the cake vanilla and lukewarm melted white chocolate.

On low speed, add the flour mixture in three additions, alternating with the buttermilk in two additions; begin and end with flour. Stop once no dry flour remains. Scrape the bowl and fold briefly to combine; do not keep beating.

Divide half of the cake batter equally between the two prepared pans, spreading it over the bottoms. Divide all of the cheesecake filling equally between the pans and gently spread it over the batter, leaving about a 1/2-inch border at the edges. Divide the remaining cake batter equally between the pans and spread it gently over the filling without swirling. Keep each pan no more than two-thirds full; if there is excess batter, bake it separately rather than overfilling.

Bake the pans side by side with space between them. Begin checking at 40 minutes; about 50 minutes is a guide, not a fixed endpoint. The tops should be set and lightly golden, and a tester in a cake-only area near the edge should show moist crumbs without wet batter. Check the cheesecake filling at the center with an instant-read thermometer: it must reach at least 160°F (71°C). Continue baking if either the cake batter or filling is not done; loosely tent the tops with foil if they brown too quickly.

Cool in the pans on a rack for about 20 minutes. Loosen the edges and carefully turn out the layers, supporting them with a plate or rack; remove the parchment. Continue cooling until no longer warm, allowing about 1 hour total cooling time. Refrigerate the supported layers for at least 2 hours to firm the filling. Refrigerate within 2 hours of baking, or within 1 hour if the room is above 90°F (32°C).

While the cake bakes, whisk the evaporated milk, frosting sugar, egg yolks, and frosting butter in a saucepan. Cook over medium-low heat, stirring constantly and scraping the bottom, until the mixture thickens enough to coat a spoon, about 10 to 12 minutes. Verify it reaches at least 160°F (71°C); do not rely on the clock alone or let it boil vigorously.

Remove from the heat and stir in the frosting vanilla, sweetened coconut, and pecans. Transfer to a shallow heatproof container and let cool until spreadable. Refrigerate within 2 hours; if chilled until firm, let it soften briefly before spreading.

Place one chilled cake layer on a serving plate. Spread about one-third of the coconut-pecan frosting over it, add the second layer, then spread the remaining frosting over the top and, if desired, the sides. Keep the cake refrigerated until serving. Cut into 12 equal slices with a sharp knife, wiping the blade between cuts.