Preheat oven to 325° F.
In a stand mixer bowl with the paddle attachment, mix the cream cheese for 1 minute on high. Add sugar and mix on high for 3 minutes. Then add vanilla, sour cream, whipped cream, and salt. Mix for 2 minutes.
In a small bowl, whisk together cornstarch and all-purpose flour with milk until smooth. Add it to the cheesecake mixture and mix until well combined.
Add ¼ cup of the filling to 5 bowls and add your food coloring and mix well. Spoon into a sandwich bag or piping bag and snip off a small tip (or fit them with round piping tips.). Set aside. Pour the rest of the filling into the crust and spread into an even layer. Tap the pan onto the counter a couple of times to get rid of air bubbles and to smooth out the surface.
Pipe your rangoli design onto your cheesecake starting from the center. Use a toothpick to help drag the colored batter to make fluid designs. Use round cookie cutters to outline your circles so that your design is as round and even as possible.
Wrap the bottom of the pan with foil and place in a large roasting pan. Fill the pan up with boiling water and bake for 45-50 minutes, making sure the cheesecake doesn't brown too much. It's done when the center is slightly jiggly. Cool completely and then refrigerate for at least 4 hours before serving.