Thoroughly clean fiddleheads and cook in a large pot of boiling water for 15 minutes, until tender. (Keeping the cover off curing cooking will help to maintain the vivid green color). Immediately rinse in cold water to stop cooking process; drain well and set aside. Start cooking pasta according to package directions.
Melt butter in a large frying pan over medium heat. Add onion and mushrooms; sauté for two minutes. Stir in garlic, fiddleheads, chicken broth or wine, basil, mustard, if using, and pepper. Bring to a boil, reduce heat and simmer for a few minutes, checking to see that the fiddleheads are tender. Add ham and parmesan cheese; stir to heat through. Drain pasta well and toss with the sauce. Serve immediately.