1. For pasta, sift flour into a mixing bowl or food processor, add basil, garlic and eggs, and mix to a smooth dough. Knead by hand for 5 minutes, or if using processor, for 1 minute. Roll dough through a pasta machine, then cut into either fettuccine or spaghetti. Lay out flat on a lightly floured work surface while preparing the sauce.
2. For sauce, precook frozen chestnuts by either boiling or steaming for 5 minutes or microwave on high for 2 minutes then fry in butter over low heat, until golden brown. Add onion, green onion and ham and fry for 2 minutes over moderate heat.
3. Stir in cream and simmer for 3 minutes or until slightly thickened. Add parsley and cheese, stirring until cheese has melted. Season to taste with freshly ground black pepper.
4. Meanwhile, cook pasta in a saucepan of boiling salted water for 5 minutes or until al dente. Drain and serve immediately with the sauce on top.