Prick the bottom of the shell and chill for 20 minutes.
Preheat oven to 400 degrees F
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.
In a small saucepan heat the apricot preserves until boiling.
Remove from heat and strain to get rid of lumps. Add the Cognac
When cool, spread a thin layer of warm apricot glaze over the bottom and sides of the tart.
Let the glaze dry between 20 - 30 minutes.
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.
Meanwhile, in a small saucepan over medium heat, heat the half-and-half until it just starts to boil and the cream foams up.
Remove from heat and gradually whisk into the egg mixture, stirring constantly.
Whisk in the Apple Brandy.
Add vanilla now and set this mixture aside while you prepare the apples.
Peel, core, and slice the apples into 1/4 inch thick slices.
Melt the 2 tablespoons butter in a large skillet over medium heat and stir in the 2 - 4 tablespoons sugar.
Add the apples and sauté until they begin to soften, approximately 5 - 10 minutes. Set the cooked apples aside.
Preheat oven to 350 degrees F
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
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.
Place the tart under the broiler in the oven just long enough to caramelize the sugar. 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.
Serve with softly whipped cream or vanilla ice cream.