Finely chop roughly half the onion, a couple of the tomatoes, 1 chilli pepper, and 2 garlic cloves. In a bowl, mix these with 2 tbsp quark, 1 egg, 2 tsp basil pesto, salt, pepper, paprika powder, and thyme. Add 500 g meat and breadcrumbs, stirring until the mixture is firm enough to shape.
Divide the meat mixture into 4 equal portions. Flatten each into a patty. Quarter the mozzarella and place one piece in the center of each patty. Fold the meat edges around the cheese to seal. Sear in a hot frying pan over medium-high heat for 1 minute on each side. Remove and wrap each steak with 2 slices of ham.
Chop the remaining onion. Heat the frying pan over medium heat and sauté the onion for 3 minutes. Add the remaining tomatoes and cook for 5 minutes. Season with salt and pepper. Pour the sauce into a baking dish with a grill insert and place the steaks on the insert above the sauce.
Bake at 180 °C (356 °F) for 25 minutes until the meat reaches an internal temperature of 63 °C (145 °F).