Bring a big pot of water to the boil, salt it as you would for pasta and drop in both the pasta and the broccoli florets.
In the meantime, in a wide pan, combine the olive oil with the anchovy (or anchovy paste), the red pepper flakes, half of the minced garlic, the black olives and a few tablespoons of the pasta cooking water. On medium-low fire, cook the seasoning stirring gently until the anchovies will have melted down, add extra pasta water if needed.
When the pasta will be al-dente drain it, preferably using a slotted spoon, onto the hot pan with the anchovy-olive seasoning, add the balance of minced garlic and saute for a couple of minutes.
Check the seasoning for salt and serve with an extra optional drizzle of extra-virgin olive oil and a nice dusting of grated Parmesan.
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