Melt the butter in a wide deep frying pan and gently sweat the garlic for a minute. Add the mushrooms and cook gently for about 10 minutes until soft. Pour in the wine, turn up the heat and allow to bubble for a few minutes to reduce a little.
Pour in the stock and season well with salt and pepper, and simmer for 10 minutes until the sauce is well reduced. Then stir through the cream, basil and parmesan and allow to cook for a couple of minutes. Taste to check the seasoning.
Whilst the ragout is cooking, bring a pan of lightly salted water up to the boil. Add the tagliatelle and boil rapidly until just tender but with plenty of bite – about 10 minutes.
To serve, toss the pasta through the sauce and pile into warmed bowls and scatter over a little extra parmesan.