Melt the butter in a saucepan over low heat.Split the vanilla bean and scrape out the seeds from one half. "Mash" the seeds on a cutting board with a bit of the sugar.Beat eggs, sugar, and the homemade vanilla sugar with an electric mixer until you have a light and fluffy mixture.When the egg mixture foams vigorously, quickly whisk in the wheat flour.When the butter is melted, remove the saucepan from the heat.Finely chop the chocolate and add it to the saucepan with the melted butter. Stir until the chocolate is melted.Add the coffee and a pinch of salt.Slowly and while stirring, pour the chocolate butter into the egg mixture.Line a springform pan with baking paper and pour the batter into the pan.Bake the cake in the oven at 175 degrees Celsius (347 degrees Fahrenheit) (fan) for 20-25 minutes.Check the cake with a wooden skewer before you take it out. The center of the cake should feel a bit underbaked, as it will set when it cools.Tap the pan lightly against the countertop when you take it out of the oven, so the cake sinks a bit.

Thaw the raspberries if you are using frozen berries.Blend the berries with powdered sugar until the mixture is completely smooth.Pass the raspberry coulis through a fine mesh sieve to remove the seeds.Pour the coulis into a bowl and refrigerate until serving.

Put the berries in a saucepan with 1/2 dl. sugar and the lemon juice.Bring the mixture to a boil and let it simmer for a couple of minutes until it softens.Blend the mixture until it is completely smooth and refrigerate it.Combine half of the heavy cream with the whole milk in a saucepan. Warm the liquid until it is lukewarm—no more than that!Put the remaining heavy cream in a bowl with the remaining sugar and the salt. Stir the mixture until the sugar is dissolved.Pour half of the warm cream/milk mixture into a bowl and add the egg yolks. Beat the mixture with an electric mixer until everything is thoroughly combined.Pour the mixture back into the saucepan with the remaining milk/cream mixture and add the cooled berry purée.Let the mixture simmer until it thickens slightly, then remove it from the heat.Pour the mixture into the cold cream/sugar mixture—it will cool faster this way—and stir thoroughly. Optionally, place the bowl in an ice bath to speed up the process.When the ice cream mixture is completely cold, you can churn it in an ice cream maker.Alternatively, you can put the ice cream mixture in a plastic container and stir it every half hour until the ice cream is frozen.

Serve the cake with the delicious blueberry ice cream and drizzle some raspberry coulis over it.