Make the tart shell:In a medium bowl, with wooden spoon or electric mixer, beat 1/3 cup butter with granulated sugar until light and fluffy.Add egg yolk; beat well.Gradually beat in flour just until blended (mixture will be crumbly).
With hands, form dough into a ball.Press evenly into the bottom and side of a 9-inch fluted tart pan with removable bottom.Bake in center of oven 12 minutes, until lightly browned.Cool on wire rack.
Make Filling:Spread nuts on cookie sheet in single layer.Bake in 375* F oven for 5 minutes, set aside to cool.Sprinkle walnuts in bottom of tart shell.In heavy 2-qt saucepan, stir sugar with butter, corn syrup and 2 Tablespoons heavy cream.Stirring constantly, bring to boiling over medium heat; boil 1 minute.Pour over walnuts.
Bake in center of 375* oven 10 minutes or just until mixture is bubbly.Place on a wire rack to cool.Meanwhile beat remaining cream, 1 Tablespoon sugar and vanilla just until stiff.Refrigerate whipped cream until serving.Serve tart at room temperature with bowl of whipped cream.
TO MAKE TARTLETS INSTEAD:Divide pastry into 16 pieces.With fingers, press evenly into 16 (2 1/2-inch) tart pans.Bake on cookie sheet(s) at 375* for 8 to 10 minutes; cool.Divide 1 cup finely chopped nuts into shells placed on cookie sheets.Pour filling into shells, dividing evenly.Bake 8 minutes, or just until filling is bubbly.Remove tarts from cookie sheets; cool on wire rack.To serve:With tip of sharp knife, loosen edge of pastry from each tart pan.Lift out gently to serving plate.Serve with chilled whipped cream.Makes 16 servings.