Reduce the oven temperature to 325°F (163°C).
Using a stand mixer fitted with a paddle attachment, beat the cream cheese until smooth, light, and fluffy.
Add the granulated sugar and beat on high speed for about 3 minutes until fully incorporated.
Mix in the vanilla extract and salt until just blended.
Add the eggs one at a time, scraping down the sides of the bowl with a spatula after each addition to ensure everything is evenly mixed.
Stir in the sour cream until fully combined, then add the heavy whipping cream and mix until smooth.
Divide the batter evenly into four separate bowls and tint each with a few drops of gel food coloring to your desired shades.
Transfer each colored batter into individual piping bags, twist the tops closed, and place the bags in a large bowl to keep them upright.
Starting with one color, snip the tip off the piping bag and pipe generous dollops of batter over the crust. Continue with the remaining colors, distributing them evenly and layering until the pan is filled to the top.
Once all the batter is in the pan, insert a knife into the batter and gently swirl it through in a swirling motion to create a tie-dye effect.
Wrap the outside of the springform pan with aluminum foil to prevent water from seeping in.
Place the wrapped pan into a deep roasting pan.
Carefully pour hot water into the roasting pan until it reaches halfway up the sides of the cheesecake pan to create a water bath.
Bake the cheesecake for 1 1/2 hours.
After baking, turn off the oven and crack the door open about 1 inch. Leave the cheesecake in the oven for an additional hour to cool gradually.
Remove the cheesecake from the oven, then loosely cover the top with aluminum foil, making sure the foil doesn’t touch the surface of the cheesecake.
Refrigerate the cheesecake for at least 4 hours, or until completely chilled and set.