In a large pot bring salted water to a boil and add the broccoli florets; cook for about 5 minutes or until bright green;
Meantime in a sautee' pan add the evoo, minced garlic, red pepper flakes (or cayenne) and anchovies filets; sautee' for 5 minutes occasionally stirring the anchovies; you may also mash the anchovies with a wooden spoon while sauteing it, until dissolved. Set the sauce aside.
With a skimmer spoon, remove all the broccoli and drain the excess water in a pasta drainer;
Add the pasta to the same water you boiled the broccoli in and cook as indicated on the box;
Add the broccoli to the saucepan with 6 TBSP of the pasta water and sautee' for 5 minutes on medium low heat;
Drain all the water from the pasta and add it to the saucepan with the broccoli. Sautee' for 4 minutes, turn the heat off, add a drizzle of evoo, toss and serve!