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1
Make the broth: Remove meat with skin from duck; keep legs intact.
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2
Cut meat into large chunks; remove excess fat, and discard.
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3
Set aside.
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4
Remove fat from bones; cut bones into large pieces.
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5
Put 6 cups water, the bones, star anise, cinnamon stick, ginger, about two-thirds of the scallions, dried shrimp, fish sauce, and sugar into a large pot.
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6
Bring to a simmer; skim foam from the surface.
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7
Cook, covered, 45 minutes.
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8
Pour through a fine sieve into another large pot; discard solids.
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9
Let broth stand 10 minutes; skim fat from the surface.
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10
Return to a simmer.
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11
Add mushrooms to broth, and cook until they are tender, about 5 minutes.
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12
Add duck meat and remaining scallions; cook until duck is heated through.
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13
Reduce heat to low, and cover.
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14
Bring a large pot of water to a boil.
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15
Add sprouts; cook until slightly softened, about 2 minutes.
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16
Using a slotted spoon, transfer to a plate.
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17
Add bok choy to pot, and cook until bright green and tender, about 5 minutes.
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18
Transfer to a plate.
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19
Bring a large pot of water to a boil.
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20
Add noodles; cook according to package instructions, 6 to 8 minutes.
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21
Drain; rinse under cold running water.
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22
Set aside.
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23
Using a slotted spoon, remove duck meat; divide among 4 serving bowls.
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24
Divide noodles, sprouts, and bok choy among bowls.
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25
Ladle broth into bowls, dividing evenly.
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26
Serve immediately.
