Finely chop the dark chocolate with a knife. Set aside 2 tablespoons for decoration. Finely chop the milk chocolate.
In a double boiler, gently melt the remaining dark chocolate and all the milk chocolate and set it aside to cool.
About half an hour before making the whipped cream, chill the beaters of your mixer and the mixing bowl you'll use to whip the cream (preferably a metal one). Once they are cold, pour the cold heavy cream into the chilled bowl and beat for 30 seconds on the lowest speed setting. Increase the speed to the highest setting and whip until the cream becomes stiff, and the beaters leave clear traces in it. Towards the end of whipping, add the powdered sugar and vanilla extract to the whipped cream. Mix until they are thoroughly combined. Do not over whip the cream, or the cream can become too dense and produce an unpleasant texture.
Divide the whipped cream into two equal parts. Add the cooled melted chocolate to one of them. Mix thoroughly.
Prepare two large dessert bowls, and alternate layers of the whipped cream mixture and the chocolate mixture in each bowl. Finish by sprinkling the finely chopped chocolate and almonds on top and add the blackberries.
Serve immediately. This dessert should not be stored for later consumption.