Heat 1/4 cup olive oil in a oven-proof sauté or saucepan over medium heat. Add the parsley, oregano, rosemary and 2 stems of basil. Cook for about 5 minutes, or until the herbs become crisp. Remove the herbs and discard. Add the onion and garlic, lowering the heat as needed so the onion cooks gently and doesn’t brown. Cook until the onions are transparent, about 5-7 minutes. Add tomatoes and their juices, crushing with a wooden spoon. Season with salt, pepper, and chili flakes. Simmer, stirring occasionally, for 30 minutes or until the sauce reduces and thickens. Stir in the heavy cream and remove from the heat.
Bring water to boil in a large stock pot. Salt and cook gnocchi until the float to the top of the boiling water. Drain and add gnocchi to the sauce. Top with the halved mozzarella balls and sprinkle with Parmesan cheese, then drizzle the tops of the gnocchi with the remaining olive oil. Broil for 5-8 minutes to melt the cheese and crisp the gnocchi. Garnish with additional basil leaves before serving.