For the dough:
In the bowl of an electric mixer, cream together sugar and butter; scrape the bowl and beaters at least once. Add egg and blend thoroughly. Add flour and mix until just incorporated. Transfer dough onto a well-floured work surface, shape into a ball, and flatten into a disk. Wrap dough in plastic wrap and chill 1 hour or overnight.
On a well-floured work surface, roll dough into a 12-inch circle. Fold in half and transfer to a 10-inch tart pan. Press dough into pan, then press off any excess dough and freeze the shell.
For the filling:
Adjust two oven racks; one to the lower shelf and the other to the center. Preheat oven to 375°.
In the bowl of an electric mixer, cream together sugar and butter until light and fluffy. Be sure to scrape down the bowl and beaters at least once. Add eggs, one at a time, and blend thoroughly. Remove from the mixer and stir in flour, nuts, and chocolate; set aside. Remove the tart shell from the freezer and spread apricot jam over the surface of the tart. Place the nut filling in large spoonfuls over the jam and spread it out evenly.
Place the tart on the lower shelf of the oven and bake 15 minutes. Lower oven heat to 350° and transfer the tart to the middle shelf; bake 15 to 18 minutes until the tart is golden and firm to the touch. Remove from oven and cool completely.
To finish the tart:
Cut the tart into 12 slices and transfer to serving plates. Whip cream, confectioners’ sugar, and jam together until it forms stiff peaks. Gently spoon some of the cream onto each slice. Place an apricot half on each slice and serve.