Heat the oil in a frying pan over a low heat, add the onion and cook, stirring occasionally, for 6–7 minutes until softened. Split the sausage open and break up the sausagemeat with a fork. Add the sausagemeat chunks and chillies to the pan and increase the heat to medium. Cook, stirring, for 4–5 minutes until the sausagemeat is golden brown.
Meanwhile, cook the pasta and broccoli in a large saucepan of salted boiling water according to the pasta packet instructions until the pasta is al dente. Don't be alarmed if the broccoli starts to break up – it needs to be very tender.
Drain the pasta and broccoli and toss into the frying pan with the sausagemeat. Stir in the pecorino and serve immediately with a bowl of extra grated pecorino on the side.