Preheat oven to 425°F with a baking stone(if you have one) placed on the rack positioned on the lowest rung.
Combine all of the filling ingredients in a saucepan, except for the eggs and yolks.Whisk the mixture over medium heat for 4-5 minutes, until the mixture begins to sputter and steam and looks smooth and shiny. Remove from heat, transfer to the bowl of a food processor. Process for one minute, scrape down the sides, and process for another minute. Stop the food processor and remove the cover. Allow the mixture to cool for 5 minutes. Return the lid, and run the processor, adding the eggs and yolks one at a time, processing for 5 seconds each time.
Pour the pumpkin mixture into the prepared, chilled pie crust.
Place the pie on the stone on the lowest rung of the oven.Bake for 15 minutes at 425°F, then rotate the pie and lower the temperature to 350°F. Bake for 20 additional minutes, watching closely for any signs of puffing. The pie should be removed from the oven when the filling is set and you should not allow it to puff, which causes dry texture and cracking.
Allow the pie to cool completely.Either chill to serve or serve at room temperature.