Genoise with Coconut Cream and Caramelized Pineapple and Mango
Using the tip of a paring knife, cut a circle into top of cake, leaving a 1/4-inch border and stopping about 1/3 inch from the cake's bottom. Insert a long slicing knife into edge of cake 1/3 inch from bottom, as if splitting the cake into two layers; instead of actually splitting the cake, only make that single incision and carefully move the knife blade within the cake to loosen the center. Repeat on opposite side. Use an offset spatula to lift out the center, leaving a shell for filling. Reserve cake center for another use.
Brush shell with simple syrup. Spread pastry cream on bottom. Refrigerate until cold, 1 hour. To serve, arrange pineapple and mango on top of pastry cream.