Preheat oven to 350 degrees F. On a lightly floured surface, roll chilled Butter Pastry from center to edges into a circle about 13 inches in diameter. Line a 9x2-inch round fluted deep tart pan that has a removable bottom with the pastry circle. Trim pastry even with top edge of pan.
For filling, in a large bowl, beat eggs with a whisk. Whisk in corn syrup, sugar, butter, vanilla, and salt. Stir in the nuts and 1/2 cup of the chocolate pieces. Pour filling into pastry-lined tart pan. Place tart pan in a foil-lined shallow baking pan. To prevent overbrowning, cover pie edge with foil.
Bake pie for 25 minutes. Remove foil. Bake for 35 to 40 minutes more or until center seems set when gently shaken. Cool on a wire rack. Serve or cover and refrigerate within 2 hours.
In a small saucepan, combine the remaining 1/2 cup chocolate pieces and the shortening. Cook over low heat, stirring constantly, until melted. Cool slightly.
To serve, remove side of tart pan. Carefully cut pie into wedges; transfer to dessert plates. Transfer melted chocolate to a clean, small heavy plastic bag; seal bag. Snip a small hole in one corner of the bag; drizzle melted chocolate mixture over pie wedges. If desired, top each serving with Sweetened Whipped Cream. Makes 10 to 12 servings.
Sweetened Whipped Cream
In a large chilled bowl, combine whipping cream, sugar, and vanilla. Beat with chilled beaters of an electric mixer on medium speed until soft peaks form (tips curl).
In a medium bowl, combine flour, sugar, baking powder, and salt. Using a pastry blender, cut in butter until pieces are pea-size. In a small bowl, beat together egg and 1 tablespoon water with a fork. Using your fingers, gently knead the mixture just until it forms a ball. (If dough won't form a ball, add another 1 tablespoon water, a little at a time.) Don't overmix; the dough should feel slightly sticky. Use your hands to slightly flatten dough into a disk about 6 inches in diameter. Wrap the disk in plastic wrap and chill in the refrigerator for 45 minutes to 1 hour or until dough is firm and easy to handle.