Preheat the oven to 350 degrees F (175 degrees C).

Roll out pie crust and gently lay inside a 9-inch pie dish. Lightly press the dough into the corners and sides of the dish to help prevent shrinkage. Prick the bottom of the pie crust a few times with a fork. Line the bottom with foil or parchment and fill with dried beans or pie weights.

Bake in the preheated oven for 20 minutes. Remove lining and beans or weights and continue baking until crust is golden brown, about 15 minutes more. Let cool completely.

Meanwhile, whisk sugar and cornstarch together in a medium saucepan. Stir in raspberries, water, and lemon juice. Bring to a boil, stirring constantly. Boil until thickened, about 5 minutes. Remove from heat; stir in butter and vanilla extract. Set aside to cool.

Pour heavy cream into the bowl of a stand mixer fitted with the whisk attachment. Beat on medium speed until stiff peaks form. Transfer to another bowl.

Combine cream cheese, powdered sugar, and vanilla extract in the stand mixer bowl. Switch to the paddle attachment and beat until well combined, about 2 minutes. Fold in whipped cream and sour cream until evenly incorporated.

Spread cream filling into the cooled pie crust. Top with the cooled raspberry topping. Refrigerate pie until thoroughly chilled, 2 hours to overnight.