Prepare Pastry for a Single-Crust Pie, if using. Flatten dough on a lightly floured surface with your hands. Roll pastry from the center to the edge, forming a 12-inch circle. For refrigerated pierces, let pastry sit at room temperature according to package directions.
Ease pastry into an 11-inch tart pan with removable bottom. Trim pastry even with the rim of the pan. Do not prick pastry.
For filling, beat eggs slightly with a rotary beater or a fork in a large mixing bowl. Stir in corn syrup. Add brown sugar, butter or margarine, and vanilla, stirring until sugar is dissolved. Stir in nuts and the 1/2 cup chocolate pieces.
Place pastry-lined tart pan on a baking sheet on the oven rack. Carefully pour filling into pan. Bake in a 350 degree F oven for 40 minutes or until a knife inserted near the center comes out clean. Cool on a rack.
To serve, cut tart into wedges and transfer to dessert plates. Melt the 1/3 cup chocolate pieces and shortening in a small heavy saucepan over very low heat, stirring constantly until chocolate begins to melt. Immediately remove from heat and stir until smooth. Cool slightly. Transfer chocolate mixture to a clean, small, heavy plastic bag. Snip a very small hole in one corner of the bag. Drizzle the melted chocolate in zigzag lines across each piece of tart, overlapping onto the plate. Cover and chill any leftover tart up to 2 days. Makes 8 to 10 servings.