Bring 3-4 l salted water (1 teaspoon salt per litre) to the boil. Wash lime hot, dry, grate peel, halve fruit and squeeze one half. Clean the chilli, cut lengthwise, remove seeds and wash. Peel garlic. Chop chilli and garlic finely. Sort rocket, wash and shake dry.
Cook the pasta in boiling salted water according to the instructions on the packet. Heat the oil in a pan. Fry the chilli and garlic briefly. Drain the noodles and collect approx. 100 ml noodle water. Put the noodles back into the pot. Mix in the pasta water, chilli and garlic oil, rocket, lime juice and zest and serve. Serve with freshly grated Parmesan cheese.