Preheat the slow cooker if necessary; see the manufacturer's instructions. Heat the oil in a frying pan, add the mince and onion and fry, stirring and breaking up the mince with a spoon until it is evenly browned.
Meanwhile, rinse the chicken livers in a sieve, drain and then chop roughly, discarding any white cores. Add to the frying pan with the garlic, pancetta or bacon and mushrooms and cook for 2–3 minutes or until the livers are browned.
Stir in the flour, then mix in the wine, stock, tomatoes, tomato purée, bouquet garni and seasoning. Bring to the boil, stirring. Spoon into the slow cooker pot, cover with the lid and cook on low for 8–10 hours.
Just before serving, add the tagliatelle to a saucepan of boiling salted water and cook for 8 minutes or until just tender. Drain and stir into the bolognese. Spoon into shallow bowls and sprinkle with Parmesan shavings and some basil leaves.