Bring a large saucepan of salted water to the boil and add the pasta and broccoli. Cook the pasta according to packet instructions until al dente. Drain.
Meanwhile heat the butter and 1 tbsp of the olive oil in a large frying pan over a medium heat. When the butter has melted and starts sizzling stir in the chilli flakes and half the garlic. Tip in the breadcrumbs and fry, stirring, until golden.
Transfer to a plate and return the pan to the heat then heat the remaining oil and garlic. Stir for a few seconds then add the drained pasta and broccoli and toss until well coated, breaking up the broccoli.
Serve scattered with the golden breadcrumbs and parmesan.