Preheat the oven to 325°F (163°C). Lightly grease the inside of a 9-inch springform pan and line the bottom with parchment paper. Wrap the outside bottom of the pan tightly with aluminum foil.
Combine graham cracker crumbs, granulated sugar, and brown sugar in a medium bowl. Pour in the melted butter and stir with a fork until all crumbs are evenly moistened. Firmly press the mixture into the bottom of the prepared pan, then bake for 10 minutes. Set aside to cool.
Bring cream cheese, eggs, and sour cream to room temperature for 45 to 60 minutes before making the filling so they blend smoothly.
Beat the softened cream cheese in a stand mixer on medium speed for 2 to 3 minutes until smooth. Scrape down the bowl, then add sugar and flour and beat for 2 more minutes. Add vanilla and sour cream and mix on low until just combined. Add eggs one at a time, mixing on low after each addition just until the egg disappears.
In a medium bowl, combine the pumpkin puree with cinnamon, ginger, nutmeg, cloves, allspice, and salt. Stir until the pumpkin is evenly coated with the spices and the mixture looks smooth.
Transfer about two-thirds of the cream cheese filling to a separate bowl. Add the entire pumpkin spice mixture to the remaining one-third of the cream cheese filling and mix on low until fully combined.
Pour the plain cream cheese filling over the pre-baked crust and spread into an even layer. Dollop the pumpkin cheesecake mixture on top, then gently smooth and swirl using an offset spatula or a toothpick in a figure-eight motion.
Place the filled springform pan on a baking sheet and bake at 325°F (163°C) for 55 to 65 minutes. The cheesecake is done when the edges are set and the center 2 inches still have a gentle jiggle. Do not open the oven door during the first 45 minutes.
Turn the oven off and leave the cheesecake inside with the door cracked open for 1 hour. Run a thin knife around the edge of the pan, then cool completely on a wire rack for another 1 to 2 hours.
Cover the cheesecake loosely with plastic wrap and refrigerate for a minimum of 6 hours, but overnight is strongly preferred for the best flavor and texture.
Run a thin knife around the edge of the cheesecake, unlatch the springform ring, and lift it straight up. Slide the cheesecake onto a serving platter. Top with whipped cream, a dusting of cinnamon, and caramel sauce if desired.