Puree 1 cup of the strawberries in a food processor or by mashing thoroughly with a fork.
In a medium saucepan, whisk together the sugar and cornstarch, then add the water and strawberry puree. Bring to a boil over medium heat, stirring constantly. Cook for 3 more minutes, until the strawberry mixture turns thick and translucent. Set aside and let cool to room temperature.
Blind bake the pie crust by rolling out the pie crust and placing it into a pie plate, trimming any excess and crimping the edges. Line the pie shell with a double layer of aluminum foil, covering the edges to prevent burning. Fill the shell with pie weights and bake at 375 degrees for 25 to 30 minutes until the pie dough looks dry and light in color. Then remove the pie weights and the foil and continue to bake until the crust is a deep golden brown, about 10 to 12 minutes longer. Remove from oven and cool completely, about 1 hour, before filling.
Meanwhile, cut any larger strawberries in halves or even fourths and place in a large bowl. Add the glaze and gently fold with a spatula until the berries are evenly coated. Fill the cooled pie crust with the strawberry pie filling, piling them into a mound and turning any cut sides to face down. If you want a "prettier" pie, you can arrange the strawberries in the pie shell first, then spoon the glaze over the top. Chill for 2 hours until set.
Prepare the whipped cream by beating the cream, powdered sugar, and vanilla with an electric mixer until smooth, thick, and nearly doubled in volume, forming soft peaks. Serve the pie with the fresh whipped cream within 5 hours of chilling for the best results.