Clean the cime de rapa (broccolini), separate the stems and the flowers. Chop the stems into bite-sized pieces. Remove the thick lower stems and set aside.
Bring a pot of water to the boil, add salt, the chopped stems and flowers. Cook for 10 minutes.
Remove the vegetables with a slotted spoon. (DON'T throw the water out!) Now, add the thick lower stems to the water and cook for 10 minutes. Remove with a slotted spoon and discard. (These stems have been used only to flavour the cooking water.) Again, keep the water – this will be used to cook the pasta later.
Gently heat a pan, add the oil and, after a few seconds, add the garlic. Add the anchovies and gently grind them until they dissolve completely.
Add the cooked cime di rapa (broccolini) and cook over medium heat for 5 minutes.
Bring the vegetable water to the boil and add the pasta. Boil until cooked.
Drain, and toss with the sauce.
Serve and season by adding optional chilli oil as desired.