Beat the cream cheese and sugars in a large bowl with an electric mixer at medium-high speed, 2 to 3 minutes, until combined and fluffy. Scrape down the sides and bottom of the bowl with a rubber spatula. Lower the mixer speed and beat in the eggs, one at a time, until just incorporated. Beat in the pumpkin, sour cream, and vanilla until combined. With the mixer on low, beat in the cornstarch, salt, cinnamon, ginger, nutmeg, and cardamom.
Bring a pot of water to a boil for your cheesecake’s water bath.
Pour the filling into the crust. Place the cheesecake in the center of a large roasting pan. Carefully pour the boiling water into the roasting pan. (The water should come about halfway up the sides of the pan).
Bake the cheesecake for 65 to 75 minutes, until the cheesecake is firm around the edges, but the center has a slight jiggle. Turn the oven off, crack the oven door just slightly (you can use a wooden spoon to keep the door slightly open), and allow the cheesecake to rest in the oven for 1 additional hour.
Carefully remove the cheesecake from the water bath. Place the springform pan on a cooling rack until it cools to room temperature. Cover and refrigerate for 12 hours.
When ready to serve, remove the sides of the springform pan and garnish the cheesecake with chopped pecans, caramel sauce or whipped cream, if you like.