Bring a pot of salted water to a boil for the gnocchi. In a skillet, heat the olive oil and finely chopped onion. Sauté until softened, then add the tomato purée. Season with salt and black pepper, and cook over low heat for about 30 minutes.

Cut the mozzarella into cubes and set aside. Preheat the oven to 350°F (180°C). Add the gnocchi to the boiling water and remove them as soon as they float to the surface. Transfer the gnocchi to the skillet with the sauce, then stir in plenty of grated Parmesan and the mozzarella cubes.

Place the gnocchi in a baking dish, top with more grated Parmesan and fresh basil, and bake for a few minutes until the mozzarella melts. Turn off the oven, carefully remove the baking dish with an oven mitt, and transfer to a serving platter.