For the broth: In a large stockpot, heat the oil over medium-high heat. Break up the duck bones and sear them on all sides until golden brown, about 5 minutes. Add the vegetables and continue cooking until caramelized, another 5 minutes. Add the spices and 16 cups water. Lower the heat and let simmer for about 3 hours. Let cool for about 15 minutes. Pass through a sieve and remove the fat. Pour the broth back into the stockpot and reserve for the duck noodle soup.
For the duck soup: Add the vegetables, the soy sauce and noodles to the stockpot with reserved duck broth and simmer for 1 minute.
To serve: Slice the duck breasts. Place the noodles in the center of a shallow bowl, top with sliced duck and pour some broth and vegetables into each bowl. Garnish with Thai basil and a slice of lime. Serve with spicy Sriracha sauce.