Prepare one foolproof pie shell, and while it chills, heat the oven to 350°F.
Cream the butter with an electric mixer on medium speed. Gradually beat in the sugars. Add the eggs individually, beating well each time. Beat in the vanilla extract and then the flour and salt until well blended. Blend in the milk, and finally stir in the chocolate chips and walnuts. Pour the filing into the chilled shell smoothing it with a spoon.
Bake the pie on the center oven rack for about 50 minutes, turning it 180 degrees halfway through. When done, the top will be dark golden, and the filling will be set except for the very center, which may jiggle slightly when you tap the pan. Cool the pie on a wire rack.