Preheat the oven to 180°C (350°F). Cut the tomatoes into thick slices and wedges. Peel and thinly slice the shallots and garlic, separating the shallot rings. Place everything in a baking dish and drizzle with the spicy olive oil, 4 tbsp of olive oil, and balsamic vinegar. Season with salt, pepper, and sprinkle with dried oregano. Mix well and bake for 20 minutes.
Drain and slice the mozzarella. Butterfly the chicken cutlets by slicing them horizontally, but not all the way through. Stuff them with mozzarella slices and basil leaves, then fold them closed.
Drain the chickpeas and add them to the baking dish with the tomatoes. Sprinkle with fresh oregano leaves, mix, and bake for another 10 minutes.
In a skillet, heat the remaining olive oil and grill the chicken cutlets on both sides, seasoning them as you cook. Finish cooking on low heat, covered, for 5 minutes.
Serve the mozzarella-stuffed chicken cutlets with the roasted tomatoes and chickpeas, garnished with fresh herbs.