Prepare pastry. In medium size bowl, with electric mixer on medium speed, beat butter and sugar until light and fluffy. Beat in egg until well mixed. Reduce mixer speed to low. Gradually beat in flour, baking powder and salt. Gather dough into a ball, flatten to a 5-inch round, and wrap tightly in plastic wrap. Refrigerate pastry at least 30 minutes or overnight.
When pastry has chilled, heat oven to 400º. Between 2 sheets of floured waxed paper, roll out pastry to a 12-inch round. Remove top sheet of paper and invert pastry into a 10-inch tart pan with removable bottom, allowing excess to extend over edge. Remove remaining sheet of waxed paper. Fold excess pastry inside so that it is even around top edge with rim of pan; press pastry against the side to make an even thickness. With fork, pierce bottom of pastry crust 10-15 times to prevent shrinkage. Line crust with aluminum foil and fill with uncooked dry beans.
Bake pastry crust 10 minutes, remove foil with beans and bake crust 5 minutes longer. Cool crust on wire rack while preparing filling. Reduce oven temperature to 350º.
Prepare filling: In heavy 1-quart saucepan, heat chocolate, butter, sugar, half and half, and salt over low heat, stirring frequently, until chocolate melts and mixture is smooth. Remove from heat.
In large bowl, with wire whisk, beat eggs slightly; slowly beat warm chocolate mixture into eggs until well blended. Spread chocolate mixture into pastry crust and bake cake 25-30 minutes.
For Topping: In double boiler melt semi-sweet chocolate squares, half and half, butter, chopped toasted hazelnuts, and hazelnut syrup, stirring constantly until smooth.
When cake has cooled, spread over top and sides. Dust with powdered sugar and serve with ice cream.