Adjust oven rack to upper-middle position and preheat oven to 450 degrees.
Line rimmed baking sheet with foil.
Spread tomatoes in sigle layer on foil and sprinkle evenly with brown sugar.
Bake until all liquid has evaporated and tomatoes begin to color, about 30 minutes.
Let tomatoes cool slightly, then peel off foil and transfer to small bowl and set aside.
Heat butter over medium heat in medium pan until foaming.
Add onion, tomato paste, and allspice.
Reduce heat to low, cover, and cook, stirring occasionally, until onions are softened, 7-10 minutes.
Add flour and cook, stirring contantly until thoroughly combined, about 30 seconds,
Whisking constantly, gradually add broth, reserved tomato juice and roasted tomatoes.
Cover, increase heat to medium, and bring to a boil.
Reduce heat to low and simmer, stirring occasionally, about 10 minutes.
Blend ingredients by using an immersion blender in pan.
Stir in quark and heat over low until hot, about 3 minutes.
Add additional broth if needed. Season with salt and cayenne to taste.
Top with cheese crumbles if desired.