Preheat the oven to 200C/180C Fan/Gas 6.
Bake the potatoes on a baking tray for 1 hour, or until soft. Scoop out the flesh and pass it through a potato ricer into a mixing bowl, or mash it thoroughly. Add the flour, Parmesan and oil and beat until smooth. Season with salt and freshly ground black pepper.
Using your hands, bring the dough together and roll it into a long sausage shape. Cut into 2-3cm/¾-1¼in length pieces.
Bring a large pan of water to the boil and cook the gnocchi for about 1 minute, or until they float to the surface. Do not crowd the pan; you may need to cook the gnocchi in batches. Lift the gnocchi out of the water using a slotted spoon and drain well.
Heat a frying pan until hot. Melt the butter, then add the gnocchi and fry until golden-brown. Set aside.
For the sauce, heat the oil in a frying pan until hot. Add the garlic and cook for 1 minute. Add the shallot and cook for a further minute. Add the nduja and courgettes, stir and cook for 4-5 minutes, or until done.
To serve, add the fried gnocchi to the sauce and cook until hot through. Serve scattered with the Parmesan and basil.