Combine 1 1/2 cups milk and pudding mix in a bowl. Beat with an electric mixer until thick. Spread pudding into pie crust.
Beat Neufchatel cream cheese, sugar, and 1 tablespoon milk with an electric mixer until smooth. Fold in whipped topping. Spread over chocolate pudding. Sprinkle with grated chocolate. Cover, and chill for at least 3 hours.