Place the salt in a large pot of water and bring to a boil.
Add the fettuccine and cook according to the package directions for al dente. During the last 3 minutes, add the broccoli. Drain, reserving 1 cup of the cooking water. Set aside.
Place the butter in the pot, reduce heat to medium-low, and stir until melted.
Add ½ cup of the reserved pasta water. Stir in ⅓ cup of the Parmesan. Add the fettuccine and broccoli and the cayenne and nutmeg, if using. Toss.
Remove from heat and sprinkle with ⅓ cup more of the Parmesan and the pepper. Toss again, adding more pasta water if the pasta is too sticky.
Serve in bowls and sprinkle with the remaining Parmesan.