Prepare the springform pan for a water bath. Once the crust has cooled, wrap the springform pan with 2 layers of heavy-duty foil wrapping and folding the edges at least ⅔ up the sides of the pan.
Combine the softened cream cheese and sugar in the bowl of a stand mixer with a paddle attachment (or use a hand mixer) and mix on medium until smooth, about 2-3 minutes scraping the sides of the bowl occasionally.
Add the eggs one at a time, mixing well after each.
Add the vanilla and salt and mix until combined, about 10 seconds.
Add the heavy cream and mix until incorporated, being careful not to overmix.
Pour the batter into the prepared pan over the crust.
Dollop half of the mango puree (about ¼ cup) over the top of the cheesecake batter. Use a knife to gently swirl the mango through the cheesecake. Some will sink down into the cheesecake.
Place the springform pan into a roasting pan and place in the oven. Carefully pour very hot water into the roasting pan until it comes about halfway up the sides of the springform pan being careful not to get any water between the pan and the foil.
Bake the cheesecake at 325 degrees for 75 minutes to 85 minutes. The cheesecake is done when the middle is still slightly jiggly but the edges are set. You can also use an instant read thermometer inserted into the center. The cheesecake should be 150-155 degrees.
Turn the oven off and prop open the oven door with a wooden spoon. Allow to cool in the oven for 1 hour.
Remove the roasting pan from the oven and remove the cheesecake from the water and foil. Cool for another hour on the wire rack.
Place the cheesecake in the refrigerator, covering the top with foil or plastic wrap and chill at least 4 hours or overnight.
Serve with the reserved mango puree.