Bring a saucepan of salted water to boil. Trim the very ends of the broccoli and discard, then chop up the rest of the stalk up to about a few centimetres from the head (or until the stalk is nice and tender).
Peel and finely slice the garlic and add this to another saucepan with a good drizzle of olive oil. Add in the chopped stalk (not the tender heads), the crushed chillies and the anchovy fillets. Cover with a lid and cook for about 10 minutes, stirring occasionally.
Add the penne to the boiling water. Make sure you stir at the beginning so the pasta doesn’t stick to the bottom. 5 minutes before the pasta is ready add the tender broccoli heads to the pasta.
Finely grate the pecorino cheese. When the pasta is cooked, scoop out a cupful of pasta water for use later and drain the pasta and broccoli. Mix this into the saucepan with the chilli and stalks and add the cheese. Add a few teaspoons of your pasta water to give the sauce the right consistency and mix thoroughly. Season with salt and pepper and serve immediately.