Carve breasts from duck, cutting along the breastbone and along curve of rib cage, pushing away with your fingers if needed to cleanly separate each breast from the bone. Cut away each breast where it meets thigh. Place on a cutting board and trim excess fat. Score fat in a diamond pattern and set aside.
Make salt cure: In a large bowl, mix salt, fennel, crushed bay leaves, peppercorns, celery seed and garlic. Put half the mixture in a shallow container. Nestle breasts in salt and cover with remaining salt. The breasts should be completely submerged in salt mixture. Cover with plastic wrap, place a heavy weight on the container to help push moisture away from the meat, and refrigerate 24 to 48 hours.
Remove breasts from the salt cure and quickly rinse any excess salt. Pat dry with paper towels. Rub a layer of fat on both sides of each breast. This will help prevent meat from drying out during the air-drying process. Sprinkle with a few peppercorns (which keep bugs away, according to Murray, when air-drying in the open) and wrap each breast like a package in at least three layers of cheesecloth. Using butcher’s string, wrap breasts using a butcher’s knot—same technique used for trussing a roast. Make sure to leave at least 12-inch piece of extra string.
Using a kitchen scale, weigh each breast and note its weight. If hanging to air dry, use string to hang from a cool, dark place. Place indoor temperature monitor nearby. Temperature should remain between 50 and 65° and the humidity should be between 60 and 70%, according to Michael Ruhlman in his book, Salumi: The Craft of Italian Dry Curing.
If using a wine refrigerator, shelves should be removable so breasts can hang inside compartment. Allow to cure for 1 to 2 weeks. Weigh regularly until breasts have lost 30% of their weight. Remove breasts from cheesecloth.
Duck prosciutto can be stored in the refrigerator for at least 2 weeks.
Tip: If you purchase a whole duck for the prosciutto, use duck legs to make confit and the remaining carcass to make stock for soup or sauces.