In the bowl of a stand mixer fitted with the paddle attachment, cream the cream cheese and sugar together on high speed for 2 minutes to ensure that it is smooth and that no cream cheese lumps remain.
24 ounces cream cheese, ½ cup granulated sugar
Add in the sweetened condensed milk and sour cream and mix until fully combined. Be sure to scrape the sides of the bowl down after mixing in each ingredient.
14 ounces sweetened condensed milk, ¼ cup sour cream
Add in the eggs, cinnamon, lime juice, vanilla, and salt and beat together for 30 seconds, then add in the cornstarch and stir for 30 seconds.
4 large eggs, 1½ tablespoons ground cinnamon, 1 tablespoon lime juice, 1 teaspoon pure vanilla extract, 1 teaspoon kosher salt, 2 tablespoons cornstarch
Divide the cheesecake batter evenly into 3 separate bowls (about 494 grams per bowl). Separately, add green, yellow, and purple food coloring to the cheesecake batters and mix well so that one bowl of batter is green, another yellow and a final bowl is purple.
Food coloring
Pour half of the purple batter into the crust. Pour half of the green batter into the center of the purple batter then pour half of the yellow batter into the center of the green batter. Repeat these steps using up the remaining cheesecake batter.
Wrap the bottom and sides of the springform pan with aluminum foil to prevent any water from seeping in. Place the wrapped springform pan into a larger baking pan or broiler pan. Fill the broiler pan with 1 inch of water to create a water bath.
Place the pans into the oven to bake for 15 minutes.
Reduce the oven heat to 250°F and allow the cheesecake to bake for 70 minutes.
Once baked, turn the heat off and leave the cheesecake in the oven with the door closed for 30 minutes. Prop the door open and let the cheesecake continue cooling for another 30 minutes.
After the hour, remove the cheesecake from the oven, unwrap the aluminum foil and place the springform pan onto a cooling rack to cool completely.
Once cooled, cover the springform pan with aluminum foil and place it into the refrigerator to chill for at least 8 hours or up to overnight.