Prepare the Dough
In a bowl, whisk together the egg, sugar, vanilla sugar, and salt.
Add softened butter and mix until smooth.
Gradually incorporate the flour, kneading into a soft dough.
Wrap the dough in plastic wrap and refrigerate for 30 minutes.
Shape and Bake the Tartlets
Preheat oven to 180°C (350°F).
Roll out the chilled dough and cut circles slightly larger than your tartlet molds.
Press the dough into the molds, trimming any excess.
Prick the base with a fork and bake for 12-15 minutes until golden.
Let the tart shells cool completely.
Make the Vanilla Pudding
In a saucepan, heat the milk over medium heat until warm.
In a separate bowl, whisk the egg yolks, sugar, and cornstarch until smooth.
Gradually pour the warm milk into the egg mixture, whisking continuously.
Return the mixture to the saucepan and cook over low heat, stirring constantly, until thickened.
Remove from heat and stir in the vanilla extract.
Let it cool slightly before filling the tartlets.
Assemble and Serve
Spoon the vanilla pudding into the cooled tartlet shells.
Chill in the refrigerator for at least 1 hour before serving.
Optionally, garnish with fresh fruit, powdered sugar, or a drizzle of chocolate.