To a stand mixer fitted with a paddle attachment, add cream cheese and sugar, beating on medium-low speed until smooth. Add sour cream, vanilla, and salt, and continue to mix on low speed until fully incorporated.
Add eggs one at a time, beating on low speed between each addition and scraping down the sides of the bowl as you go. Mix until just combined.
Pour half the cheesecake mixture into the baked crust. Add spoonfuls of the cranberry sauce and swirl into the cheesecake filling with a knife or toothpick. Top with the remaining cheesecake batter and the remaining cranberry sauce, and swirl again.
Tap the pan on a flat surface to remove any air bubbles. Place in a large roasting pan and carefully pour the boiling water ½ the way up the springform pan.
Bake for 55 minutes or until the edges are set, and the center is slightly jiggly.
Turn the oven off and open the door, allowing it to slowly cool down for about 1 hour. Then, transfer to a wire rack to cool completely. Once cooled, cover with plastic wrap and refrigerate for at least 8 hours or overnight.
Gently run a knife around the edges of the pan and carefully release the ring of your springform pan.