Add the softened cream cheese, brown sugar, and granulated sugar to a mixer bowl. Mix with a paddle attachment on medium low speed until smooth, 1-2 minutes. Scrape down the bowl with a spatula.
Add the eggs, one at a time, letting each egg incorporate before you add the next. Scrape the bowl again once all the eggs have been added.
With the mixer off, add the pumpkin puree, sour cream, vanilla, all the spices, and the salt, then sprinkle the flour over the top. Turn the mixer to medium low and mix until just combined.
Pour this pumpkin cheesecake mixture into the prepared crust, then place this pan inside a deep roasting pan. Boil some water in a kettle, then pour the boiling water into the roasting pan, to come up halfway up the sides of the foil wrapped cheesecake pan.
Carefully, transfer this to the middle rack of the oven. If you find it easier, you can place the roasting pan with the cheesecake in it in the oven first, then pour the boiling water into the oven.
Bake for 1 hour, then turn the oven off, prop open the oven door a little with a wooden spoon, and keep the cheesecake in the oven for another hour.
Once one hour has passed with the cheesecake in the turned off oven, remove from the oven and the roasting pan, and let it cool for an hour at room temperature.
Transfer to the fridge, and let it sit for at least 3-4 hours in the fridge, preferably overnight.