To make the pastry: Stir 1 1⁄3 cups of flour and salt together in a medium bowl. Add butter, 1 egg yolk, and water; stir until mixture forms large crumbs. If it is too dry to press a handful together, stir in more water. Press dough into a ball and wrap in plastic wrap. Flatten slightly and refrigerate for at least 30 minutes, or until firm.

To make the frangipane: Cream butter and 1/2 cup of sugar together in a medium bowl with an electric mixer until light and soft. Gradually mix in an egg and remaining egg yolk one at a time. Stir in apple brandy. Stir 2 tablespoons of flour into ground almonds, then mix into batter. Set aside.

Roll out pastry dough into a 12-inch circle on a lightly floured surface. Fold loosely into quarters, and center the point in a 10-inch tart or pie pan. Unfold dough, and press into the bottom and up the sides. Prick with a fork all over, and flute the edges. Return pastry to the refrigerator to chill until firm.

Preheat the oven to 400 degrees F (200 degrees C). Place a baking sheet inside the oven while it preheats.

Spoon frangipane into chilled pastry crust, and spread into an even layer. Arrange apple slices in an overlapping spiral pattern. Each slice should have one edge pressed into the frangipane until it touches the pastry base, and then overlap the previous slice. Start at the outside edge, and work towards the center.

Place the pie plate on top of the baking sheet in the preheated oven. Bake until filling begins to brown, about 15 minutes. Reduce the oven temperature to 350 degrees F (175 degrees C). Bake for another 10 minutes, then sprinkle sugar over the top of the tart. Return to the oven until the sugar caramelizes slightly, about 10 minutes more.

Cool the tart on a wire rack. A short time before serving, warm the apricot jelly; add some water if necessary to make it a liquid consistency. Brush warm jelly over the tart for a nice shine.