You can leave the sausages in their casings and cut them into lengths the size of half your index finger, or you can remove the casing and break the sausage meat into chunks the size of a walnut.
Add the garlic and chilli and cook for another couple of minutes, then throw in the broccoli. Stir all this around and return the sausages to the pan.
Pour in the vermouth (or wine). Bring to the boil then turn the heat down, season, cover the pan and cook over a medium heat for about 7 minutes. The broccoli will become tender and the sausages cooked through.
Remove the lid and continue to cook so that the juices around the sausages and vegetables becomes a bit thicker. It shouldn’t be soupy but you want it to coat the pasta.
Cook the pasta in plenty of boiling, lightly salted water until al dente. Drain and add it immediately to the sausages. Season again and serve with grated Parmesan if using.