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 add ½ teaspoon of vanilla extract. Mix until a soft dough forms, then press it evenly into the bottom of a 9-inch tart pan. Chill the tart base in the refrigerator for 30 minutes to firm up.

While the tart base chills, whisk together 3 egg yolks, 2 whole eggs, and 1 cup of white sugar in a saucepan. Gradually stir in ⅓ cup of cornstarch until smooth, then add 2½ cups of whole milk and 1⅓ cups of heavy cream. Heat over medium heat for about 10 minutes, stirring continuously until the mixture thickens and bubbles gently. Remove from heat and stir in 7 oz of chopped dark chocolate until completely melted and smooth.

Preheat your oven to 350°F (175°C). Carefully pour the rich chocolate custard into the prepared tart shell, smooth the surface with a spatula. Place the tart pan on a baking sheet to catch any drips, then bake in the preheated oven for 30-35 minutes, or until the center is just set but still slightly wobbly.

Once baked, remove the French chocolate flan from the oven and let it cool at room temperature for about 1 hour. After cooling, brush the top lightly with 1 tablespoon of jam to create a glossy finish. Once completely cooled, refrigerate for at least 3 hours to firm up the custard before serving.

Once chilled, carefully slice the flan with a sharp knife. For a beautiful presentation, serve each slice with fresh berries or a dollop of whipped cream.