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Melt the butter and chocolate then mix them to obtain a homogeneous texture.
Whisk the sugars and eggs for 5 minutes until the mixture becomes foamy and doubles in volume.
In a mixing bowl, mix the flour and yeast then pour everything into the egg and sugar mixture.
Add the chocolate and melted butter. Mix everything until you obtain a homogeneous texture. Gradually add the milk.
Preheat the oven to 180°C.
Spread melted butter using a brush over the entire surface of the bundt cake mold.
Pour the dough into the mold then tap it lightly on the work surface to release any air bubbles.
Bake for 45 minutes. Insert a knife to check the cooking, it should come out dry. At the end of cooking, unmold the bundt cake onto a rack and let it cool completely.
Crush the chocolate into small pieces.
Boil the cream then pour it over the chocolate.
Mix using a Maryse until you obtain a homogeneous texture.
Pour the icing onto the bundt cake all at once.
Bring the blackberry balsamic vinegar with the sugar to the boil and remove from the heat as soon as the sugar has dissolved. You get a liquefied syrup texture.
Pour this syrup over the blackberries and leave to macerate.
Serve the cake with a little crème fraîche and fruit with balsamic vinegar.