- In a small saucepan, bring the frozen berries and sugar to a boil over medium heat for about 5 minutes. 
- Transfer the berries to a bowl with a spoon, leaving the berry juice in the pot. 
- Mix the starch with the water until smooth. Add the red juice to the pot with the berry juice and bring to a boil.  
- Stir in the starch mixture once it boils, then remove from the heat. Add the berries back into the pot and mix with the thickened juice. 
- Preheat the oven to 180°C (top/bottom heat) or 160°C (fan oven).  Grease a loaf pan and dust it with semolina to prevent sticking. 
- For the cake, cream together the soft butter, sugar, and vanilla sugar in a large bowl. Beat in the eggs, one at a time. Mix in the quark until fully combined. 
- In a separate bowl, whisk together the pudding powder, flour, semolina, baking powder, and salt. Gradually add the dry ingredients to the quark mixture, mixing until smooth. 
- Wash the lemon thoroughly in hot water, dry it, and grate the zest. Stir about 1 teaspoon of lemon zest into the quark mixture for added flavor. 
- Pour half of the cake mixture into the prepared loaf pan, then add a layer of the berry mixture. Top with the remaining mixture. 
- Bake the cheesecake for about 60–70 minutes, or until a skewer inserted in the center comes out clean. Let the cheesecake cool completely in the pan before removing. Slice and enjoy!