Preheat the oven to 350 degrees. Spray an 8-inch round cake pan with cooking spray. Line the bottom of the pan with parchment paper, then generously spray the pan with cooking spray again. Set pan aside.

Beat the cream cheese, sugar, and flour together with an electric mixer set to medium speed. Beat in eggs and egg yolks one at a time, mixing until eggs are just incorporated. Turn mixer to low and beat in the sour cream, cream of coconut, rum flavor and coconut extract. Fold in the toasted coconut.

Pour batter into the prepared pan and smooth the top. Set pan in a roasting pan (or any large baking pan) and carry over to the oven. Pour a couple inches of water into the pan, then carefully transfer to the oven. Bake 28 to 34 minutes, until the center of the cheesecake barely wobbles. Remove from the oven and immediately run a knife between the cake and the edge of the pan. Cool cheesecake to room temperature. Once cooled, cover with plastic wrap and refrigerate overnight.

After the cheesecake has refrigerated, dip the pan in a bowl of hot water for about 15 seconds. Run a knife around the edge of the cake again, then set a large plate or a cake circle on top of the pan. Invert the cake onto the plate. Keep refrigerated until you assemble the cake.

Spray 2 8-inch round cake pans with cooking spray. Line the bottoms with parchment paper; spray the paper and lightly dust with flour. Set pans aside.

Prepare cake batter according to the directions on the box, substituting pineapple juice for the water—if your cake mix calls for 1 cup of water, use 1 cup of pineapple juice. Beat in the vanilla pudding mix, then the pineapple flavoring and food coloring, if using.

Divide evenly between the prepared cake pans and bake as directed on the box, until a cake tester inserted into the center of the cake layers comes out clean. (The layers may take just a few minutes more than usual to be fully done.) Cool in pans on a wire rack for 30 minutes, then carefully invert pans onto the rack to cool cake layers completely.

In a stand mixer fitted with the paddle attachment, beat the butter until it is light and fluffy, about 2 minutes. Beat in the cream of coconut. Turn mixer to low and gradually add 4 cups powdered sugar, then the rum (if using), rum flavor, coconut extract, and salt. Beat on medium for 4 minutes. Adjust consistency if necessary by adding additional cream of coconut if frosting is too thick or additional powdered sugar if it is too thin.

Place one of the pineapple cake layers on a cake stand or cake circle. Spread a thin layer of frosting over the top. Carefully top with the cheesecake layer. Top cheesecake with another thin layer of frosting, spreading it gently into an even layer. Top with remaining pineapple cake layer. (It’s possible your cheesecake layer will be a little wider than your cake; if this is the case trim it by running a sharp paring knife around the perimeter of the cake.) Use remaining frosting to frost the cake, and decorate if desired. Serve and enjoy.