Preheat the slow cooker if necessary; see the manufacturer's instructions. Heat the oil in a large frying pan, add the sausages and fry, turning until browned but not cooked through. Transfer to the slow cooker pot with tongs.
Drain off the excess fat from the pan to leave 2 teaspoons, then add the onion and fry until softened. Mix in the mushrooms and garlic and fry for a 1–2 minutes.
Stir in the chopped tomatoes, stock and a little salt and pepper and bring to the boil, stirring. Pour the mixture over the sausages, cover with the lid and cook on low for 8–10 hours or until cooked through.
When almost ready to serve, bring a large saucepan of water to the boil, add the tagliatelle and cook for 7–8 minutes or until just tender then drain. Lift the sausages out of the slow cooker pot and slice thickly, then return to the pot with the pasta and mix together. Sprinkle with torn basil leaves and grated Parmesan, if liked. Serve with a green salad.