Heat the oil and fry the onion, carrot, celery, garlic and mushrooms for 5-10 minutes until softened. Add the remaining ingredients except the mince and cook for 15-20 minutes until the sauce has thickened.
Place the pasta in a large pan of boiling water and cook according to the pack instructions. Drain but save 3-4 tablespoons of the cooking water.
Meanwhile stir in the mince into the tomato sauce and heat through for 3-4 minutes, adding a little of the pasta cooking water if required.
Serve the spaghetti Bolognese topped with the cheese and basil.