Cut the broccoli heads into small pieces and blanch with the leaves for 5 minutes. Drain well, reserving the blanching water.
Heat 2 tbsps of the olive oil in a heavy bottomed saucepan and gently fry the onion until golden. Add the garlic and anchovy fillets , and stir to break up the anchovies- they will melt into a sauce.
Add 1 ladleful of the blanching water and the broccoli. Cook for 5 minutes then add the pine nuts and olive pieces and continue to cook over a gentle heat for 5 minutes to combine the flavours. Season.
Cook the penne in boiling salted water until al dente then drain. Add to the sauce along with the basil, Pecorino and remaining olive oil. Serve.