Add the egg and cold water, and knead quickly until the dough forms a ball. Wrap it in plastic wrap and refrigerate it for at least 30 minutes.
Meanwhile, prepare the pastry cream. In a saucepan, heat the milk with the split vanilla pod (or vanilla extract) until it reaches boiling point. Remove from heat and let steep for about 10 minutes.
In a bowl, whisk the egg yolks with the sugar until the mixture turns white. Add the flour and mix well.
Remove the vanilla pod from the hot milk. Pour the hot milk over the egg mixture while whisking constantly.
Return the mixture to the saucepan and cook over low heat while stirring constantly until it thickens and reaches the consistency of custard. Take off heat and let cool.
Preheat your oven to 180°C (350°F).
On a lightly floured work surface, roll out the dough into a circle the size of your pie pan. Transfer it to the buttered tart pan and prick the bottom with a fork.
Spread the pastry cream on the cooled tart base.
Arrange the apple slices on the pastry cream in a decorative manner.
Bake the pie in the preheated oven for about 30 to 35 minutes, or until the crust is golden and the apples are tender.
While the tart cools slightly, lightly heat the apricot jam in a saucepan until liquid. Gently brush the apples with it to give them a nice shine.
