Bring a large pan of salted water to a boil and add the broccoli and spaghetti. Simmer for 5 minutes. Drain and reserve 240ml (1 cup) of the cooking water.
Meanwhile heat 1 tablespoon of oil in a large frying pan over a medium heat and add the garlic and chilli and lemon zest. Cook gently for a few minutes until fragrant, then add the spaghetti, broccoli and the cooking water to the frying pan.
Stir everything together and leave to bubble for a few minutes in order to reduce the water and finish cooking the pasta and broccoli. Add the lemon juice, some seasoning and check to see if everything is tender.
Serve immediately in warmed bowls, with an extra grating of lemon zest, some sliced chilli and a drizzle of extra virgin olive oil.
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