Preheat the oven to 450 degrees F. Line a 9-inch springform pan with two sheets of parchment, pressing it in and letting it stand well above the rim.
Blend the Batter
Beat the room-temperature cream cheese with the granulated and brown sugars until completely smooth.
Add the eggs one at a time, then mix in the pumpkin, heavy cream, cornstarch, cinnamon, ginger, nutmeg, cloves, vanilla, and salt until silky. Do not overmix.
Bake
Pour the batter into the lined pan. Bake at 450 degrees F for 50 to 55 minutes, until the top is deeply browned and the center still jiggles noticeably.
Cool and Chill
Cool completely in the pan on the counter. Chill at least 4 hours or overnight, then bring back toward room temperature before slicing and serving.
Notes
Room-temp cream cheese: Cold cream cheese leaves lumps that will not blend out.
Pull it jiggly: A firm center out of the oven means a dry cake once cooled. It sets as it chills.
Serve just below room temperature: Cold from the fridge mutes the custardy texture.