Cook the asparagus and sugarsnap peas in a saucepan of boiling water for 3–4 minutes, then drain and refresh under cold running water. Drain well and set aside.
Cook the pasta in a large saucepan of salted boiling water according to the packet instructions until al dente.
Meanwhile, halve the courgettes lengthways and cut the mushrooms in half. Heat the oil in a large frying pan, add the onion and garlic and cook for 2–3 minutes. Add the courgettes and mushrooms and cook, stirring, for 3–4 minutes. Stir in the asparagus and sugarsnap peas and cook for 1–2 minutes before adding the lemon juice and herbs.
Drain the pasta and return to the pan. Add the vegetable mixture and mozzarella and season to taste with salt and pepper. Toss gently to mix and serve.