In a medium saucepan, combine 2 cups strawberries with the sugar, water, lemon juice, and cornstarch. Using an old-fashioned potato masher, mash the strawberries until the mixture is nearly a liquid with some pieces of berry remaining. Pour the remainder of the fresh strawberries into the full baked pie crust and set aside.
Heat the mashed berry mixture over medium heat, stirring occasionally, 3-5 minutes. When the mixture starts to bubble around the edges, stir constantly until bubbling throughout and thickened, 3 minutes. When done, the mixture will have slow, large bubbles and be thick.
Remove from the heat and immediately pour over the fresh strawberries in the pie shell. Allow to cool to room temperature, 1 hour. Place in the refrigerator until fully chilled, 4-6 hours. Serve with fresh whipped cream.