Place the pie crust in a 9-inch pie dish and crimp the edges. Prick the bottom lightly with a fork, then bake according to the crust instructions until lightly golden. Let it cool while preparing the filling.
In a medium saucepan, whisk together the brown sugar, cornstarch, and salt until evenly combined and free of large lumps.
Gradually whisk in the milk, followed by the egg yolks, until the mixture is smooth. Place the saucepan over medium heat.
Cook, whisking constantly, until the mixture thickens into a smooth pudding-like consistency and begins to gently bubble. Continue cooking for another minute, then remove from the heat.
Stir in the butter and vanilla until completely melted and incorporated. For an extra-smooth filling, strain it through a fine mesh sieve before pouring it into the cooled crust.
Pour the warm butterscotch filling into the pie crust and smooth the surface. Cover the surface loosely with plastic wrap and refrigerate for at least 4 hours, or until completely set.
Beat the heavy cream, powdered sugar, and vanilla until soft peaks form. Spoon or pipe the whipped cream over the chilled pie, then add a light drizzle of butterscotch sauce if desired. Slice and serve cold.