Prepare your pumpkin by scooping out the seeds and pulp, place it on a baking sheet, do not put the top of the pumpkin (stem) on the sheet just yet.
Preheat oven to 400 degrees.
In a mixing bowl combine the sugar, eggs, and vanilla and whisk until combined.
Add the heavy cream, cornstarch, and salt and whisk until fully combined.
Pour mixture into your prepared pumpkin (allowing about 3/4 of an inch space between the filling and the top of the pumpkin and begin baking it.
Bake at 400 degrees uncovered.
After 15 minutes, cover the top of the pumpkin loosely with foil (don't let it touch the top of the custard or it will stick and "ruin" the appearance) and bake another 15 minutes.
Lower oven temp to 375, place the top of the pumpkin on the tray and continue baking for 15 minutes more. Remover the foil and bake an additional 30 minutes or until a knife inserted into the custard comes out mostly clean.
Turn off the oven, allow the pumpkin to cool for an hour, then place it in your cold garage (loosely covered with wrap or foil) or your refrigerator and allow the custard to set 6 hours or overnight. When ready to serve, scoop out custard into small dishes (you can scrape the sides a bit as you scoop it out if you choose to scrape off some of the cooked pumpkin for additional flavor, I am sure the Pilgrims wasted nothing).