In a mixing bowl, combine 1 cup of all-purpose flour, ⅓ cup of icing sugar, ¼ cup of cocoa powder, and ¼ teaspoon of salt. Pour in 1 stick of melted butter and ½ teaspoon of vanilla extract, then mix until you form a soft dough. Press the dough evenly into a tart pan and refrigerate for at least 30 minutes to firm up.

Preheat your oven to 350°F (175°C). Remove the tart shell from the refrigerator, then bake it in the preheated oven for 15-20 minutes, or until the edges are firm and the center is set. Once baked, allow it to cool on a wire rack while you prepare the chocolate custard.

In a medium saucepan, whisk together 3 egg yolks, 2 whole eggs, 1 cup of white sugar, ⅓ cup of cornstarch, and ½ teaspoon of salt until smooth. Gradually whisk in 2 ½ cups of whole milk and 1 ¾ cups of heavy cream. Cook over low heat, stirring continuously, until the mixture thickens and coats the back of a spoon, about 10-15 minutes.

Once the custard has thickened, remove the saucepan from the heat and add in 7 ounces of chopped dark chocolate. Stir until the chocolate has completely melted and the custard is silky and smooth. Keep stirring for a minute longer to ensure everything is well combined.

Carefully pour the luscious chocolate custard into the cooled tart shell, smoothing the top with a spatula to create an even layer. Make sure the custard fills the shell without spilling over the edges.

Return the filled tart to the oven and bake for 30-35 minutes, or until the custard is just set but still slightly jiggles in the center. Once done, remove it from the oven and let it cool to room temperature.

Once cooled, brush the top of the French Chocolate Flan with 1 tablespoon of warmed jam for a glossy finish. Chill in the refrigerator for at least 2 hours before serving. Slice into pieces and enjoy!