Preheat the oven to 240°C/Fan 220°C/ Gas 9. In a roasting tin, mix the mushrooms and chestnuts with the capers, garlic, butter, salt and pepper. Place in the oven for 20 minutes, covered, taking out half way to stir.
Mix the sauce ingredients together and season.
Bring salted water to the boil and cook the tagliatelle until soft. Drain, but keep some pasta water to loosen the sauce.
Heat the rapeseed oil in a pan and add the courgette noodles. Cook until softened. 5. Add the pasta to the sauce and the courgetti. Serve with the mushrooms, chives and Parmesan shavings.