Preheat the oven to 325 degrees Fahrenheit. Add the cream cheese to a large mixing bowl and mix thoroughly for about 2 minutes or until the cream cheese is smooth.
Add the caramel sauce, granulated sugar, and brown sugar. Mix the eggs in one at a time, then add the vanilla extract. Finally, add the sour cream. Mix the filling until just combined, making sure there are no lumps. Scrape the inside of the bowl to ensure you combine all the ingredients.
Now it's time to prepare the water bath. Double-wrap the bottom of the springform pan with tin foil. Make sure that no water can get into the pan. Move the pan into a larger pan--I use a 10x14 metal cake pan. You can also use a roasting pan. Pour hot water into the large pan until it reaches about an inch in depth. Make sure there is half an inch to a full inch of space between the top of the larger pan and the water.
Bake the cheesecake in the middle rack of the oven for 65-75 minutes. You'll know the cheesecake is done when the edges start to move away from the pan and the middle of the cheesecake is a little wobbly if you move or shake it.
Once baked, turn the oven off, remove the springform pan from the water bath, put the cheesecake back in the oven, and crack the oven door a few inches. Leave the cheesecake in the gradually cooling oven for 1-2 hours. Then move the cheesecake to room temperature for another 30-60 minutes before covering it with tin foil or plastic wrap and moving to the fridge. Chill in the fridge for 4 hours or overnight.