Press the quark through a fine sieve into a bowl. Stir in 2 tablespoons of brown sugar and the milk for about 1-2 minutes until smooth. Drain the sour cherries.
Crumble the pumpernickel into a bowl. Sprinkle the remaining brown sugar over it, pour the kirsch over the bread, and add the grated chocolate. Mix for about 1 minute until well combined.
In a glass bowl, create alternating layers of pumpernickel mixture, quark, and cherries. Repeat the layers until all ingredients are used. Refrigerate for at least 2 hours, then serve with vanilla sauce or sweet cream.