Heat the oven to 350°F. Grease and parchment-line the bottom of a 9-inch springform pan, then beat the softened cream cheese and sugar until smooth. Add the egg and vanilla, mixing just until combined, and bake the cheesecake layer for 25–30 minutes until set but slightly soft in the center.

Cool the cheesecake completely, then chill or briefly freeze it until firm enough to handle. Grease two 9-inch round cake pans and divide the melted butter and brown sugar between them.

Arrange drained pineapple rings in the pans and place a maraschino cherry in the center of each ring. Reserve 1 cup of pineapple juice, adding water if necessary to reach the full amount.

Beat together the yellow cake mix, instant vanilla pudding mix, pineapple juice, vegetable oil, and eggs until smooth. Divide the batter between the prepared pans without disturbing the pineapple arrangement.

Bake the cake layers at 350°F for 25–30 minutes, until a toothpick inserted into the cake portion comes out clean. Cool them in the pans for about 10 minutes, run a knife around the edges, and invert them onto racks to cool completely.

Place one pineapple cake layer pineapple-side down on a serving plate. Add the cold cheesecake layer, top with the second pineapple cake layer pineapple-side up, and refrigerate until thoroughly chilled before slicing.