Trim the edge of the dough with the rolling pin. Prick the shell with a fork and chill the shell for 30 minutes.
Preheat the oven to 350 degrees F and preheat the baking sheet.
In a bowl with the mixer cream the butter, add 1/4 cup plus 2 teaspoons of the sugar, and beat the mixture until fluffy. Add the egg, beating well, and beat in the almonds and the vanilla. Spread the frangipane mixture in the shell, top it with the apricot halves cut sides up, and bake the tart on the baking sheet in the lower third of the oven for 40 minutes, or until the filling is golden and set.
Preheat the broiler.
Sprinkle the tart with the remaining 2 teaspoons sugar and put it under the broiler about 6 inches from the heat for 2 to 3 minutes, or until the filling is browned. Brush the tart with the apricot glaze, let it cool, and remove the rim of the pan.
In a large bowl with your fingertips or with two knives blend the flour, sugar, salt, and the butter until the mixture resembles meal. Add the egg and 1 tablespoon of the water, toss the mixture until the liquid is incorporated, adding 1 more tablespoon of water if the mixture is dry, and form the dough into a ball. Knead the dough lightly with the heel of your hand against a smooth surface for a few seconds to distribute the fat evenly and re-form it into a ball. Dust the dough with flour and chill it, wrapped in waxed paper, for 1 hour.
PBTE SUCRIE: PROCESSOR METHOD: In a food processor fitted with the plastic or steel blade combine the flour, sugar, salt, and butter and process the mixture until it resembles coarse meal. In a bowl combine the egg with 1 tablespoon of the water and sprinkle it over the flour mixture. Process the mixture until it comes together in large pieces about the size of pebbles and transfer the dough to a work surface. If the mixture is dry, sprinkle it with 1 more tablespoon water. With the heel of your hand knead the dough against a smooth surface for a few seconds to distribute the fat evenly and form it into a ball. Dust the dough with flour and chill it, wrapped in waxed paper, for at least 1 hour or for up to 2 days. Yield: about 15 ounces dough or enough dough for one 10-inch shell
Recipe courtesy of Gourmet Magazine