In a pot over medium heat, combine pumpkin puree, brown sugar, sugar, salt and spices (cinnamon, ginger, nutmeg and cloves). Bring mixture to a simmer for 5 minutes.
Remove pot from the heat and stir in the heavy whipping cream and vanilla.
Add eggs, one at a time, mixing well after each addition. Finally stir in cornstarch until combined.
Bake the pie at 400° F for 15 minutes, then reduce temperature to 350° F and bake for 40 minutes.