Rinse the broccoli under cold water. Cut into florets. Discard the stalks. In a large pot of boiling water, blanche the broccoli for about one minute. Remove with a skimmer. Set the broccoli aside. Retain the cooking water for the pasta.
Preheat the oven to 350 F.
Add salt and return the retained cooking water to a boil. Cook the fusilli until very al dente (half of the recommended cooking time). Drain pasta and place with the broccoli in a mixing bowl (now retaining about a cup of the cooking water). Coat with olive oil and salt and pepper.
Mix in the scamorza and add the cream (if using it) or some of the pasta cooking water. Mix well and move the pasta and broccoli to a large baking dish. Sprinkle the top with Parmigiano.
Bake for 30 minutes, with the last 5 minutes under the broiler, until the top is golden.