To make the pâte sucrée: Add the flour, sugar and salt to the bowl of a food processor. Pulse to combine. Add the butter and pulse again until the mixture is crumbly. Add the egg yolks and pulse again until combined. While the food processor is running, slowly add the water starting with 2 tablespoons and adding a 3rd if needed, until the mixture just comes together.
Remove the dough to a work surface and knead gently to bring it together into a smooth ball. Shape the pastry into a flat disc and wrap it in plastic wrap and refrigerate for 45 minutes (alternatively, it can be frozen and then thawed in the refrigerator when needed).
Roll out the chilled pastry on a lightly floured surface until it is about ⅛-inch thick. Carefully wrap the pastry around the rolling pin and then gently unfold it over a 9-inch fluted tart pan with a removable bottom. Gently fit the pastry into the pan against the sides (without stretching it) and trim away excess dough. Prick the bottom with a fork. Place the crust in the fridge for at least 1 ½ hours to stop shrinkage when baking.
Preheat the oven to 180°C. Place the oven rack in the center of the oven. Line a baking sheet with foil or parchment paper in case of leaks.
Remove chilled crust from the fridge, line the pastry with parchment paper and fill with pie weights or uncooked beans or rice. Blind bake the crust for 10 minutes. Remove the parchment and weights and continue to bake for another 10 to 12 minutes, or until pale golden. Remove from the oven and cool on a rack for about 15 minutes until room temperature.
For the frangipane filling: In the bowl of an electric mixer fitted with the paddle attachment, combine the butter and sugar until light and creamy, a couple minutes. Then add the ground almonds and mix until smooth. Finally add the eggs and combine well, scraping down the sides periodically to ensure the mixture is smooth. Spoon the frangipane filling into the tart shell, smoothing it out evenly.
Starting from the outside, arrange the apple slices in a spiral pattern, overlapping one another until the entire surface is covered.
Place the tart onto the preparing baking sheet and transfer to the 350°F (180°C) oven. Bake for 5 minutes and then brush the top with the melted butter (use a blotting motion so you don’t displace the apple slices from how they are arranged).
Continue to bake for about 40 minutes longer until the filling begins to brown at the edges. Then lightly brush the top with some of the beaten egg and return to the oven for another 10 to 15 minutes (giving you a total of about 50 to 55 minutes baking time).
To make the glaze, heat the apricot jam and water in a small pan and strain into a bowl. Remove the tart from the oven and, while still warm, use a pastry brush to coat the apples with the warm glaze. Serve either warm or at room temperature plain, with crème fraiche or vanilla ice cream.
