Preheat your oven to 325°F (160°C). In a mixing bowl, combine graham cracker crumbs, ½ cup of granulated sugar, and ½ cup of melted unsalted butter until well combined. Press this mixture firmly into the bottom of a 9-inch springform pan. Bake for 8-10 minutes until lightly golden, then remove from the oven and let it cool completely while you prepare the cheesecake filling.

In a large mixing bowl, beat together four packages of cream cheese and 1 cup of granulated sugar on medium speed until creamy and smooth. Add in 1 cup of sour cream, 1 teaspoon of vanilla extract, and three large eggs, mixing in one egg at a time. Finally, pour in ¾ cup of cream soda, and blend everything together until just combined and smooth, being careful not to overmix.

In a small saucepan over medium heat, combine ½ cup of heavy cream, ½ cup of brown sugar, and ¼ cup of unsalted butter. Stir the mixture until completely melted and combined, then remove from heat and add 1 teaspoon of vanilla extract. Divide this butterscotch mixture into four separate bowls, and use gel food coloring to achieve vibrant red, yellow, blue, and green colors, carefully mixing each until the dye is fully incorporated.

Pour the smooth cheesecake filling over the cooled crust, using a spatula to evenly spread it. Drizzle the colored butterscotch mixture in a swirl pattern across the cheesecake. Using a skewer or knife, gently swirl the colors into the filling to create a marbled effect. Bake the Hogwarts Houses Butterbeer Swirl Cheesecake for 50-60 minutes, or until the edges are set but the center still jiggles slightly when you gently shake the pan.

Once baked, turn off the oven and leave the cheesecake inside with the door slightly ajar for about one hour to cool gradually. After this, refrigerate the cheesecake for at least 4 hours or overnight to achieve the best texture. Before serving, garnish as desired and slice, using a warm knife for clean cuts.