Preheat your oven to 350°F (175°C). This ensures even baking for both the pineapple upside down cheesecake layers.

Melt one stick of butter in a 9-inch round metal cake pan (you can place it in the preheating oven). Sprinkle the light brown sugar evenly over the melted butter, mixing gently to combine. Arrange the drained pineapple slices in a single layer, fitting about 7-10 slices. Place a maraschino cherry in the center of each pineapple ring and fill gaps with additional cherries for a beautiful pattern.

Prepare your yellow cake batter according to package or recipe instructions. Mix the instant cheesecake pudding powder into the dry ingredients for enhanced flavor. Pour the batter over the pineapple arrangement, filling the pan about two-thirds full.

Bake at 350°F for 40-60 minutes, checking with a toothpick starting at 40 minutes. The cake will take longer than usual due to the caramelized topping. Once done, let cool in the pan for 10 minutes, then carefully invert onto a plate. Allow to cool further while you prepare the cheesecake.

Combine graham cracker crumbs, melted butter, brown sugar, and a pinch of salt in a bowl. Mix until the crumbs are evenly moistened and hold together when squeezed. Press the mixture firmly into the bottom of a 9-inch springform pan. Bake at 350°F for 5 minutes, then remove and let cool slightly.

Beat the softened cream cheese and granulated sugar until smooth and creamy using an electric mixer. Add eggs one at a time, beating on low speed just until incorporated after each addition (avoid overmixing). Mix in vanilla extract and a pinch of salt. Pour the filling over the pre-baked graham cracker crust.

Wrap the bottom of the springform pan tightly in aluminum foil to prevent water leaks. Place the springform pan inside a larger baking pan. Pour hot water into the larger pan until it reaches about halfway up the sides of the springform. Bake at 350°F for 50-70 minutes until the center is slightly wobbly but mostly set. Turn off the oven, crack the door open, and let the cheesecake cool slowly. Refrigerate for at least 4 hours, preferably overnight.

Once both components are ready, carefully cut the pineapple upside-down cake horizontally in half using a steady, rotating motion. Use two spatulas to gently lift one cake half (pineapple side up) and center it directly on top of the chilled cheesecake. Gently press down so the layers adhere together. Chill the assembled Cheesecake Factory pineapple upside down cheesecake for 1-2 hours before serving.

Use a large, sharp knife warmed under hot water for clean cuts. Wipe the blade between slices for the prettiest presentation.