Reduce your oven temperature to 375. In a large bowl, whisk together your entire can of pumpkin puree, brown sugar, white sugar, salt, cinnamon, ginger, cloves, nutmeg, and allspice until just combined. Whisk in the eggs, one at a time, and then add the vanilla extract and whisk until everything is smooth. Add in your heavy cream, and whisk until it's well combined and there are no streaks of white running through the mixture. Optionally, use an immersion blender to further mix your filling for 1-2 minutes, or just until everything is extra smooth.