Bring a large saucepan of salted water to the boil and tip in the broccoli and pasta. Cook for about 14 minutes, or according to the pasta packet instructions, until the pasta is al dente and the broccoli is cooked and starting to fall apart.
Meanwhile, pour the oil into a large frying pan and add the anchovies, crushed chillies and garlic and heat over a very low heat for 5–6 minutes until the anchovies have melted into the oil.
Drain the pasta, reserving a ladleful of the cooking water, and toss the pasta and broccoli into the pan with the anchovy oil. Toss over a high heat for 30 seconds, then pour in the reserved cooking water and continue stirring over the heat for a further 30 seconds. Work the Parmesan into the pasta, then serve with an extra scattering of Parmesan.