Prepare your pumpkin by scooping out the seeds and pulp, place it on a baking sheet.
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.
Bake at 400 degrees covered in foil for 30 minutes.
Lower oven temp to 375, remove the foil, continue baking for 45 minutes more 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 the fridge to allow the custard to set 6 hours or overnight.
When ready to serve, scoop out custard into small dishes, scrape the sides a bit as you scoop it out to scrape off some of the cooked pumpkin.