Preheat your oven to 325°F. Wrap the outside of a 9-inch springform pan with two layers of heavy-duty aluminum foil to safeguard against leaks.
Pour the first ¼ cup of melted butter directly into the bottom of the springform pan, tilting it to coat the base evenly. Sprinkle the brown sugar uniformly over the butter layer.
Arrange the drained pineapple slices flat on top of the brown sugar, fitting as many as you can in a single layer. Place a maraschino cherry into the center opening of each pineapple ring.
In a large mixing bowl or the bowl of a stand mixer, beat the softened cream cheese and granulated white sugar together on medium speed for 2 to 3 minutes until smooth and completely free of lumps.
Add the sour cream, vanilla extract, and 2 tablespoons of the reserved pineapple juice, mixing until fully incorporated.
Turn the mixer to low and add the room-temperature eggs one at a time, mixing just until combined after each addition to avoid incorporating too much air.
Pour the smooth cream cheese filling directly over the arranged pineapple rings and cherries in the pan, smoothing the top flat with a spatula.
In a small bowl, toss the graham cracker crumbs with the remaining ¼ cup of melted butter until the mixture resembles wet sand. Gently press the buttery crumbs into a uniform layer over the top of the cream cheese batter. This will serve as the bottom crust once the cake is inverted.
Place the springform pan into a large roasting pan. Pour boiling water into the roasting pan until it reaches halfway up the sides of the springform pan to create a gentle, insulating water bath.
Bake at 325°F for 60 to 70 minutes, or until the edges are set and matte but the center retains a slight jiggle. Turn off the oven, crack the door open a few inches, and let the cheesecake cool inside the water bath for 1 hour.
Remove the pan from the water bath, discard the foil, and run a thin knife along the inside edge of the pan. Refrigerate for at least 6 hours (or overnight) to allow the cake to firm completely.
To serve, carefully remove the springform ring. Place a large serving platter upside down over the graham cracker crust, and firmly invert the cake in one swift motion. Slowly lift away the bottom base of the pan to reveal the glossy, beautifully caramelized pineapple topping. Slice and serve cold.