Simmer duck meat. In a 6- to 8-quart pan, combine duck, broth, and 2 tablespoons curry paste. Cover pan and bring to a boil over high heat. Simmer until leg meat is tender enough to pull from bones, about 2 hours. Lift out duck and let cool to touch. Skim and discard fat from broth. Reserve 1 1/4 cups broth; use remainder for other dishes. Pull meat from bones; discard fat, skin, and bones. Tear meat into bite-size pieces. If making up to 2 days ahead, cover broth and meat airtight and chill.
Make green curry sauce. In a 5- to 6-quart pan, mix the 1 1/4 cups duck broth, remaining curry paste, coconut milk, fish sauce, sugar, curry powder, and chili flakes. Bring to boiling on high heat, then add potatoes. Cover and simmer until potatoes are tender when pierced, about 40 minutes.
Add duck meat and simmer gently until hot, 5 to 10 minutes. Stir in minced cilantro. Ladle into wide bowls, garnish with cilantro sprigs, and add salt to taste.
Per serving: 579 cal., 28% (162 cal.) from fat; 33 g protein; 18 g fat (9 g sat.); 59 g carbo (fiber not available); 874 mg sodium; 99 mg chol.