Heat the milk with the vanilla until boiling point.
Beat the sugar with the eggs and cornstarch.
Slowly pour the hot milk over the egg mixture, whisking constantly.
Transfer the mixture to the saucepan and cook over low heat, stirring constantly, until the mixture thickens.

Remove from heat, remove the vanilla pod, and add the chocolate.
Let it rest for 2 minutes before mixing the preparation with a whisk until the chocolate is fully melted.
Cover the chocolate cream with plastic wrap and let it cool completely.

While the cream is cooling:
Butter a 9-inch (23cm) diameter tart mold.
Roll out the pastry on a floured surface and place it in the mold.
Reserve for 30 minutes in the freezer.
Preheat the oven to 350°F (180°C) and place the grill in the middle of the oven.
Remove the tart mold from the freezer and pour in the cooled chocolate cream.
Smooth the top with a spatula and bake for 1 hour.

Remove from the oven and let cool on a cooling rack.
Unmold and store this flan in the refrigerator. Serve chilled.