Put a big kettle of water on for the pasta. (When water boils, dribble in the pasta, stiring, and cook until al dente. Drain, return to pot and keep warm).
While all this is going on, tear the prosciutto into irregular pieces about 2" square. Combine with cream in a large saucepan and cook over low heat for 8 to 10 minutes: it should bubble very gently; do not let it boil. Add green onions and cayenne and cook about 5 minutes more, then stir the remaining vegetables into the saucepan and cook until they are just tender, 6 or 7 more minutes.
Pour onto pasta, put pan over medium heat and toss until all is well mixed. Season to taste with additional cayenne and salt, then serve at once on warmed plates. Pass cheese separately. Serves four as a main course or eight as a first course.