Fill a large pot with water and bring it to a boil over high heat.
While the water is coming to a boil, place a pan on medium heat and add a knob of butter.
Once the butter has melted, add the anchovies and chili flakes to the pan. Cook them together for about 2 minutes, stirring occasionally.
After 2 minutes, add the minced garlic to the pan.
Cook the garlic with the anchovies and chili flakes for another 2 minutes, or until the garlic becomes fragrant and slightly golden.
Now, add the broccoli florets to the pan with the anchovies, chili flakes, and garlic.
By this time, your water should be boiling. Add the pasta to the boiling water and cook it according to the package instructions (usually around 5-10 minutes, depending on the type of pasta).
Continue cooking the broccoli with the other ingredients in the pan, stirring occasionally, until the broccoli becomes tender but still crisp, about 4-5 minutes.
Once the pasta is cooked, drain it in a colander to remove excess water.
Add the drained pasta to the pan with the cooked broccoli, anchovies, chili flakes, garlic, and butter sauce.
Toss everything together gently until the pasta is evenly coated with the sauce.
Plate the broccoli and anchovy pasta and serve it immediately while it's still hot.
Enjoy your delicious broccoli and anchovy pasta! Feel free to garnish it with some grated parmesan cheese or freshly ground black pepper if desired.