Place 1 quart of the strawberries, the sugar and cornstarch into a medium sauce pan on low heat. Mash the strawberries with a potato masher.
Add the rest of the ingredients and stir constantly over medium heat while the mixture is thickening. The mixture will become very thick and have a clear sharp red color in about 15 minutes. Turn off the heat and set aside.
Cut the caps off of the other quart of strawberries and place them in the precooked pie crust, flat side down, so that they completely cover the bottom of the crust.
Pour the cooked strawberry sauce on top of the raw strawberries. Cool for at least 3 hours before devouring.
Optional: the pie can be topped with a non-dairy topping, if you like, just before serving.