Beat cream cheese and 1 tablespoon heavy cream together in a bowl.
Spread into bottom of pie crust. Arrange about 2 cups quartered strawberries onto cream cheese layer.
Mix 2 cups mashed strawberries, 1 cup sugar, and cornstarch in a saucepan; cook over medium heat until slightly reduced and thickened, about 10 minutes. Cool completely.
Pour cooled strawberry mixture over strawberry layer in pie crust. Chill in refrigerator until set, 2 hours.
Beat 1 cup heavy cream, 2 tablespoons sugar, and vanilla extract in a bowl until light and fluffy, about 5 minutes.