Cook the spaghetti in boiling salted water, according to packet instructions.
Cut the broccoli into small florets and put aside. Thinly slice the thick stalks and cook in a pan on low heat with anchovies, butter, chillies, and garlic, for about 8-10 minutes. Cook the florets with the pasta for 4 minutes.
Drain the pasta and broccoli florets, reserving some pasta water, and add to the pan. Stir gently and add 2 tbsp reserved water and a sprinkling of parmesan cheese.
Salt and pepper to taste.
Serve hot and with another sprinkling of parmesan.