In a mixing bowl, combine all-purpose flour, icing sugar, cocoa powder, and salt. Pour in the melted butter and vanilla extract, stirring until a smooth dough forms. Press this mixture evenly into a tart pan, ensuring the base and sides are well covered. Chill the tart shell in the refrigerator for 30 minutes to firm up.

Whisk together the egg yolks, whole eggs, white sugar, cornstarch, and salt in a saucepan. Gradually pour in the whole milk and heavy cream while continuously whisking to avoid lumps. Heat the mixture over medium heat, stirring frequently, until it thickens and coats the back of a spoon (about 8-10 minutes). Once thickened, remove from heat and stir in the chopped dark chocolate until fully melted and smooth.

Pour the rich chocolate custard into the chilled tart base, spreading it evenly. Preheat your oven to 350°F (175°C) and place the filled tart pan on a baking sheet. Bake for about 30-35 minutes until the center jiggles slightly.

After baking, let the flan cool at room temperature. Cover with plastic wrap and refrigerate for at least 4 hours, preferably overnight.

Before serving, brush the top of your chilled French chocolate flan with a thin layer of jam for a shiny finish. Cut neat slices and serve as is or with chocolate shavings or fresh berries.