Heat oil in a wide pan. Add onion, garlic, chili, and anchovies, cooking over low heat and stirring constantly for 5 minutes. Add the broth, then salt and pepper to taste. Add the broccoli florets and bring to a boil. Cover and cook over low heat for 15 minutes or until the broccoli is cooked but still firm.
Bring water to boil in a large stock pot. Salt and cook pasta according to package instructions before draining and returning to the pot or a serving dish. Toss with Broccoli sauce and top with freshly grated cheese to serve.