In a large oven-safe skillet, over medium heat, add oil, whole thyme, oregano, and rosemary sprigs. Using tongs, gently stir and turn the herbs until they are covered in oil, and cook for about 3-5 minutes, or until the herbs begin to crisp.
Remove the herbs and discard. Add shallots and garlic, lowering the heat to medium-low to gently cook for 2-3 minutes, until tender and fragrant.
While the aromatics cook, in a medium-sized bowl crush the whole tomatoes with your hands and add to the pan with the juices. Stir in the chopped rosemary, strained tomatoes, wine, Sicilian spice, salt, and pepper. Let the sauce simmer for 30-40 minutes, or until the sauce reduces and thickens, stirring occasionally.
Once the sauce has thickened, remove from the heat, stir in 1/2 of the half and half until combined, and pour the remaining half and half into the center of the sauce without stirring.
About 10 minutes before the sauce has finished, start boiling a medium-sized pot of water. Once the water is boiling, add the gnocchi and boil until they begin to float to the surface about 3 minutes. Drain the gnocchi in a colander and then add to the center of the sauce.
Preheat the oven broiler to high. Using a wooden spoon, gently push some of the gnocchi into the sauce so they are not all piled above the sauce. Top with halved bocconcini and sprinkle Parmesan cheese evenly over the surface.
Broil the dish for about 5 minutes, until the cheese melts and becomes bubbly and toasted. Sprinkle Sicilian spice, chopped thyme and oregano over the dish to finish.