Photograph: Philip Webb
Put the dried mushrooms in a small, deep bowl, add boiling water to just cover, then leave to soak. Bring a large pan of salted water to the boil. Toast the walnuts in a deep frying pan for 2-3 minutes, tossing now and then – they will smell toasted when they're ready – tip into a bowl and leave to cool.
Cook the sliced mushrooms in the frying pan with the oil for 8-10 minutes, stirring now and then – the mushrooms will release liquid as they cook. Drain the dried mushrooms (reserve the soaking liquid), chop them and add with the liquid to the sliced mushrooms. Bubble together for 5 minutes to reduce the liquid to a couple of tablespoons. Season. Tip the mushrooms into a bowl, rinse and dry the pan.
Cook the pasta in the boiling water according to pack instructions. Fry the sage leaves in a frying pan in a tablespoon of the walnut oil until crispy. Drain on kitchen paper; sprinkle with salt.
Drain the pasta, return to the pan and toss with the lemon zest and juice and the mushrooms. Serve in warm bowls, drizzled with the remaining walnut oil and sprinkled with the walnuts and crispy sage leaves.
Get ahead: make the mushroom ragu and toast the walnuts up to a day ahead.
Kitchen secret: you could also add shredded cooked chicken to the pasta mixture at the end, if you like.