Heat the olive oil in a large skillet over medium heat. Add the parsley, oregano, rosemary and basil stems and cook for about 5 minutes or until the herbs become crisp. Remove the herbs and discard. Add the chopped onion to the oil, lowering the heat and continue cooking until the onions are transparent, about 5-7 minutes. Add garlic and cook until fragrant. Tear the whole tomatoes into small chunks and add them and their juices to the pan along with the onion broth. Season with salt, freshly ground black pepper and red pepper flakes. Simmer for about 45 minutes or until the sauce reduces and thickens, stirring occasionally. Stir in the heavy cream and remove from the heat.
Meanwhile, preheat the broiler. Bring a large saucepan of salted water to the boil. Add the gnocchi to the water and cook until they float to the surface, about 2 to 3 minutes; drain well. Transfer the gnocchi to the sauce and stir to coat. Top with the bocconcini and grated Parmesan cheese. Place the skillet under the broiler for about 3 to 5 minutes or until the cheese melts and gnocchi become crispy. Garnish with additional fresh basil leaves and serve immediately.