Preheat Oven to 350˚F.
In your food processor, blend the softened cream cheese, and brown sugar on medium speed until light and fluffy and without lumps (5 minutes), scraping down the sides once to make sure you don’t have chunks of cream cheese.
In a separate bowl, using a whisk, stir together pumpkin puree, eggs, sour cream, flour, pumpkin pie spice, salt, and vanilla extract. Mix until well combined. Add this mixture to the cheesecake filling and continue blending on low speed just until well combined, scraping down the sides as needed.
Transfer filling into the pre-baked crust, and bake on the middle rack at 350˚F for 1 hour. Turn off heat, prop the oven door open slightly with a wooden spoon, and let cheesecake sit in the oven another 45 minutes.
Then remove from the oven, and let cool to room temperature before covering with plastic wrap and refrigerating. Serve when fully chilled (at least 4 hours in the refrigerator, or overnight).
Before serving, carefully remove cheesecake from the springform pan by running a blunt knife along the sides of the cheesecake to release it from the sides of the pan. Add desired toppings, and serve.