Pour the morello cherries and their liquid into a saucepan, reserving 50 ml of juice and setting aside 4 whole cherries. Heat over medium heat and bring to a boil.
In a small bowl, mix the cornstarch with the reserved 50 ml cherry juice to create a smooth slurry.
Once the cherries reach a boil, stir in the cornstarch mixture. The sauce will thicken as it bubbles. Remove from heat and let cool for about 10 minutes.
Whip the cream using an electric mixer or whisk until stiff peaks form, about 2-3 minutes.
In a separate bowl, mix the quark with sugar, stirring for 1-2 minutes until smooth.
Using a spatula, gently fold the whipped cream into the quark mixture until combined.
Chop the chocolate bar into small pieces.
Divide the quark cream, thickened cherries, and chopped chocolate among four tall glasses. Layer in each glass as follows: quark cream, thickened cherries, chocolate, quark cream, reserved cherries, chocolate, quark cream. Top each glass with one reserved cherry and a few chocolate pieces.
Serve immediately or refrigerate. Covered and refrigerated, the dessert will keep for up to 1 day.