Bring a large pan of water to the boil, add salt, stir and then add the broccoli and cook until tender. Lift the florets from the water with a slotted spoon and set aside. Keep the cooking water for the pasta.
In a large frying pan, warm the olive oil or guanciale over a medium-low flame and gently fry the chilli and garlic – peeled and crushed for a mild flavour, chopped for stronger flavour – until fragrant. At this point, you can discard the garlic if you want.
Crumble the sausage meat into the pan and stir until the meat is brown all over. Add the wine, raise the heat and let the pan bubble for few minutes until the wine has evaporated away. Add the cooked broccoli and stir.
Meanwhile, bring the water back to the boil, add the pasta and cook until al dente. Using a slotted spoon, lift the cooked pasta, and the residual water that clings to it, into the frying pan.
Add the cheese and stir again, then serve, passing round more grated cheese for those who want it.