Heat 1 tbsp oil in a large, deep pan over medium-high heat. Add the sausage and fry until it builds up a golden crust, using your wooden spoon to crumble as you go. Remove the sausage and place in a bowl to one side, leaving the excess fat in the pan.
At this point you can pop your pasta in salted boiling water and cook until al dente. Don't drain it.
Lower the pan heat to medium and fry the chilli flakes, black pepper and garlic for 30 seconds or so (be careful it doesn't burn). Pour in the wine, and raise the heat to a rapid simmer. Reduce it down for 4-5 minutes, deglazing the pan with your wooden spoon as needed. It's important to reduce the wine so it doesn't end up too strong. A lot of it should evaporate and the pungent smell of alcohol should vanish.
Pour in the stock then stir in the broccoli. Simmer and stir occasionally for another 4-5 minutes, or until the broccoli is al dente and the stock has reduced (adjust the heat if you need to).
Turn the heat to low and use a slotted spoon to transfer the cooked pasta straight from the pot into the pan. Add the sausage and give everything a good stir. Scatter over the butter, then pour in a good splash of the leftover pasta water (~1/3 cup). Swiftly stir until the butter melts and emulsifies with the liquid.
Add a good squeeze of lemon juice and the parmesan and continue stirring until you've got a very light, glossy sauce that clings to the pasta. It shouldn't be watery at all. If it is, continue tossing to thicken and reduce. If it dries out at all, just stir in another splash of pasta water.
Check for seasoning and adjust if needed, then serve with extra parmesan and enjoy!