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Preheat oven to 350 degrees.
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Chill unbaked pie crust in freezer for 15 minutes before using.
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Cream the butter with an electric mixer on medium speed. Gradually beat in the sugars.
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Add the eggs individually, beating well each time.
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Beat in the vanilla, then the flour and salt until well blended.
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Blend in the milk (don't worry if the filling looks a little lumpy at this point) and finally, stir in the chocolate chips and walnuts.
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Pour filling into the chilled shell, smoothing it out with a spoon.
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Bake the pie on the center oven rack for about 50 minutes, turning it 180 degrees halfway through baking time.
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When done, the top will be dark golden brown, and the filling will be set except for the center, which may slightly jiggle when you tap the pan.
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Cool pie on a wire rack. Serve warm, at room temperature, or chilled.