Bring a medium to large pan of generously salted water to boil, add the pasta and simmer until al dente. This normally takes 10-12 minutes. (Note 6)
Meanwhile, set a large frying pan to a medium heat, add the olive oil and sauté the garlic and chilli for 1-2 minutes.
Add the chopped sausage and fry for a few more minutes until cooked.
Add the broccoli and fry for 2 minutes.
Pour the chicken stock into the pan and leave to simmer on a medium to high heat until the broccoli is tender and stock has evaporated.
At this point, the pasta should be al dente. Reserve a cup of the pasta water before you drain it with a colander.
Add the cooked pasta to the broccoli / broccolini and sausage mixture and mix and stir in the butter.
Add the reserved pasta water a tablespoon at a time if required to moisten the pasta.
Serve with freshly ground black pepper and freshly grated Parmesan.