Beat Cream Cheese: In a large bowl, beat the softened cream cheese at medium speed for 3 minutes until creamy.
Add Sugars: Mix in the brown sugar and granulated sugar and beat for another 2 minutes. Scrape down the bowl to ensure everything is well combined.
Add Sour Cream: Mix in the sour cream and scrape the bowl again.
Mix Eggs and Flavorings: Add the eggs one at a time, mixing just until incorporated. Avoid over-mixing. Add the vanilla extract and salt, then mix briefly.
Assemble: Pour the cheesecake batter over the cooled crust, spreading it evenly.
Bake in Water Bath: Place the pan in a larger roasting pan. Pour hot water into the roasting pan to create a water bath. Bake at 325°F for 55-65 minutes. The center should jiggle slightly, and the edges should be set.
Cool Slowly: Turn off the oven and leave the cheesecake inside with the door closed for 1 hour. Then refrigerate for at least 6 hours or overnight.