Pastry Crust:  Roll out the pastry and fit it into a 8 or 9 inch (20 to 23 cm) tart pan (instructions for how to roll out the pastry are given in the recipe for the Sweet Pastry Crust).  Prick the bottom of the shell and chill for 20 minutes.  

Preheat oven to 400 degrees F (205 degrees C) and place rack in center of oven.  Line the unbaked pastry shell with parchment paper or aluminum foil.  Fill tart pan with pie weights or beans, making sure the weights are to the top of the pan and evenly distributed over the entire surface.  Bake crust for 20 to 25 minutes until crust is dry and lightly browned.  Remove weights and cool crust on wire rack.  When cool, spread a thin layer of warm apricot glaze over the bottom and sides of the tart to seal the crust and prevent it from getting soggy.  Let the glaze dry between 20 - 30 minutes.

Apricot Glaze: In a small saucepan heat the apricot preserves until boiling.  Remove from heat and strain to get rid of lumps.  Add the Cognac or water.  

Brandy Custard: In a large bowl whisk the flour and sugar together.  Mix in the eggs and stir with a wooden spoon to make a smooth paste.   Do not let this mixture sit too long as it will form a crust. 

Meanwhile, in a small saucepan over medium heat, heat the half-and-half with the vanilla bean until it just starts to boil and the cream foams up. Remove from heat, take out the vanilla bean, and gradually whisk into the egg mixture, stirring constantly.  Whisk in the Apple Brandy.  At this point, scrape out the seeds from the vanilla bean and add to egg mixture or, if using vanilla extract, add it now.  Set this mixture aside while you prepare the apples.

Apples: Peel, core, and slice the apples into 1/4 inch thick slices.  Melt the 2 tablespoons (26 grams) butter in a large skillet over medium heat and stir in the 2 - 4 tablespoons (25 - 50 grams) sugar.  Add the apples and sauté until they begin to soften, approximately 5 - 10 minutes.  Set the cooked apples aside.

ASSEMBLE TART:

 Preheat oven to 350 degrees F (177 degrees C) and place rack in the middle of the oven. Arrange the apple wedges in concentric circles on top of the cooled and glazed tart shell.    Carefully pour the custard over the apples to just below the top of the tart pan (do not fill all the way or the custard will drip between the crust and the pan).  Sprinkle lightly with the Cinnamon Sugar.

Place tart pan on a larger baking sheet to make it easier to remove from oven and bake for about 25-30 minutes or until the custard has set.

Let the tart cool on wire rack, then lightly sift powdered sugar over the top.  Place the tart under the broiler in the oven just long enough to caramelize the sugar on the apples.  To prevent the edges of the tart shell from over-browning, you can cover them with a thin piece of aluminum foil or pie shields.  Be careful not to over brown.

To remove the tart from the fluted sides of the pan, place your hand under the pan, touching only the removable bottom not the sides. Gently push the tart straight up, away from the sides.  The fluted tart ring will fall away and slide down your arm. If you want to remove the bottom of the pan, run a knife or thin metal spatula between the crust and metal bottom, then slide the tart onto a cardboard cake round or platter.  

Serve with softly whipped cream or vanilla ice cream.

Makes 1 - 8 or 9 inch (20 or 23 cm) tart.

Sources:

Friberg, Bo. 'The Professional Pastry Chef'. Third Edition. Van Nostrand Reinhold. New York: 1996.