Bake one refrigerated pie crust according to package directions. Let it cool completely.
Mash 1½ cups of the berries with a fork and combine with the sugar, vanilla, and ¼ cup of water in a medium saucepan over medium heat. Bring to a low boil, stirring and mashing frequently, and cook until the fruit begins to soften and break down more, about 5 minutes.
Whisk together the cornstarch and ½ cup of water in a small bowl. Stir the cornstarch mixture into the simmering strawberry mixture and return the mixture to a boil over medium-high heat. Reduce heat to medium-low and simmer until thickened, about 3 minutes, stirring frequently. Remove from the heat and fold in the remaining fresh strawberries. Immediately transfer the strawberry mixture to the pie crust.
Let cool slightly, about 15 minutes, then place in the refrigerator to cool completely, about 4 hours.