In a small skillet over medium heat, toast the pine nuts for a couple of minutes until golden. Remove from heat and set aside.
In a large skillet over medium heat, sauté the onion in olive oil until golden. Add the broccoli and mix together for a couple of minutes. Add the vegetable broth and cover. After 2-3 minutes, remove about half the broccoli and set aside. Cover the remaining broccoli and cook for 2-3 more minutes until soft. Use an immersion blender to purée the broccoli and broth mixture until smooth. Add salt and pepper to taste.
Cook the pasta until al dente (about 2 minutes less than the package directions), drain and retain 1 cup of the cooking water. Add the pasta to the pot containing the broccoli puree and mix thoroughly. Add the broccoli florets, the anchovies and most of the pine nuts. Add some of the retained cooking water if it seems too dry.
Serve with the remaining pine nuts and grated Parmigiano.