Place a large pot of water over high heat to boil for cooking the pasta and broccoli.
In a large skillet, heat oil over medium heat.
Add garlic, anchovies, and onions. Cook until softened and anchovies melt into the oil.
Add wine to deglaze pan. Reduce until almost dry. Add pepper flakes. Keep pan on low while you cook pasta.
Heavily salt the boiling water.
Drop in pasta and broccoli. Cook until the pasta is al dente.
Drain pasta and add to the skillet. Add pasta water and grated cheese. Cook until the sauce, pasta and cheese become one. Add as much pasta water as necessary. Season with salt and pepper to taste.