On a lightly floured work surface, roll out the pie crust to a 12-inch (30 cm) circle about ¼-inch (6mm) thick and line a 9-inch (23cm) pie dish with it. Crimp the edges and refrigerate while you prepare the filling.
In a large mixing bowl by hand (or with an electric mixer), beat the butter and sugar together on High until light and fluffy, about 3 minutes.
Whisk in the eggs, then the flour and salt.
Add in the buttermilk, lemon juice, and vanilla extract and mix until smooth.
Brush the edges of the crust with the egg wash, pour in the filling and bake for about 50 minutes, until the filling is lightly browned and set on the edges but still jiggly in the center.
Let cool to room temperature before serving. Store any leftovers well covered in the refrigerator for up to 2 days. This pie is also delicious served cold.