Heat the oil and butter in a large frying pan, add the onion and cook for 10 minutes until soft and golden. Add the garlic, chilli flakes and anchovies and cook for a further 2–3 minutes or until the anchovies begin to disintegrate. Mash them with the back of a spoon, pour over the cream and season.
Meanwhile, cook the broccoli in a large saucepan of salted boiling water for 3 minutes, then remove with a slotted spoon. Add the pasta to the pan of boiling water and cook according to the pack instructions until al dente.
Stir the broccoli into the anchovy sauce, cover with a lid and cook for 3–5 minutes or until the broccoli is cooked through.
Drain the pasta, reserving a little of the cooking water, and stir through the broccoli sauce, adding a little cooking water to loosen if needed. Serve immediately.