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Boil the spaghetti for 1 min. Add the broccoli and cook for 4 mins more.
Meanwhile, heat the oil in a frying pan and add the shallots and garlic. Gently cook for 5 mins until golden. Add the chillies and sage to the pan and gently cook for 2 mins. Drain the pasta, mix with the shallot mixture in the pan, then scatter with Parmesan, if you like.