Puree the 2 cans of peeled tomatoes. Chop the onion finely and mash the garlic clove. Finely chop the fresh basil, thyme, oregano, and rosemary. Combine the chopped onion, mashed garlic, and chopped herbs with the tomato puree.
Bring the tomato sauce to a boil in a large pot over high heat without a lid. Boil for 15-20 minutes until the sauce becomes thick and shiny. Reduce heat to medium-low. Stir in honey and butter to taste (optional). Simmer for at least 1 hour for the best flavor.
Heat the oil in a pan with high sides over high heat until shimmering. Wash the chicken breast fillets and trim away any fat and tendons. Fry them for 3-4 minutes per side over high heat until golden. Season both sides with salt, pepper, and paprika. Pour the tomato sauce over the chicken and simmer over medium heat for 8-10 minutes until the chicken is almost cooked through.
Cut the fresh tomato into small cubes and remove the skin and seeds if needed. Stir the tomato cubes and capers into the sauce. Season the sauce with salt, pepper, and paprika to taste.
Cut the mozzarella into thin slices. Arrange the mozzarella slices over each chicken fillet. Cover the pan and simmer over medium heat for 3 minutes until the cheese has melted and the chicken reaches an internal temperature of 74°C (165°F).
Plate the chicken with tomato sauce and mozzarella, and serve with pasta (such as fettuccine or linguini), rice, or baguette.