Roll out half the dough 1/8 inch thick on a floured surface and cut out four 6-inch rounds, reserving scraps. Fit rounds into tart pans measuring 4 inches across the top and 3/4 inch deep and, using a rolling pin roll over the pan edges to trim excess dough. Roll out remaining dough in same manner, cut out 4 more rounds, reserving scraps, and repeat procedure with reserved scraps, cutting out 4 more rounds. (Alternatively, dough maybe fitted into two 9-inch tart pans with removable bottoms.)
In small bowl set over barely simmering water melt chocolate, stirring occasionally, until smooth. Brush it onto bottoms of the shells, chill shells
15 minutes. Divide 1 3/4 cups walnuts among shells. (If using 9-inch tart pans, divide 2 1/2 cups walnuts between the shells.)
In large heavy skillet cook sugar over moderately high heat, stirring constantly with fork, until it is melted completely and a deep golden caramel. Remove skillet from heat and add the corn syrup. Cook mixture, stirring, until it is smooth. Stir in the butter, stirring until it is melted.
In a bowl whisk together eggs and vanilla. Add the caramel mixture in a
slow stream, whisking. Whisk mixture until it is combined well. Divide mixture among shells, coating walnuts completely. Bake the tartlets on the baking sheets in the middle of a preheated 375ºF. oven 35 to 40 minutes,
or until pastry is pale golden. Transfer tartlets to racks and let them cool. (May be made 1 day in advance and kept at room temperature.) Serve tartlets with the whipped cream and grated chocolate. Serves 12.