Wash and pat dry the duck legs. Rub the duck legs with the first 6 ingredients, and marinate for an hour for the flavors to blend well.
Preheat over to 450 degrees. Shake off the marinade from the duck legs. Place the duck legs in foil-lined baking tray, and roast for 15-20 minutes until the skin is golden brown. Remove from the oven.
In the meantime, soak the dates and shitake in room temperature for 15 minutes to hydrate them. Remove and squeeze dry.
Prepare the pickled green papaya (or green mango or Granny Smith green apple). Slice into very thin pieces and marinate with 1/4 cup white vinegar with a pinch of sugar and a pinch of salt.
In instant pot, add all the soup ingredients including the soaked dates and shitake mushrooms and the duck legs. Close the lid, set pressure cook on high for 10 minutes. When done, release steam manually. (If using a regular pot, put all the broth ingredients in a large pot, heat to boiling. Add the roasted duck legs, lower the heat to simmer and cook for around one hour and half. Make sure to add more water to replace the evaporated liquid.)
In the meantime, cook the noodles in boiling water according to package instructions, and divide in 4 bowls
When steam has been fully released, open the lid and cancel pressure cook function. Skim any fat rising to the top. Remove the duck legs and put one duck leg in each bowl. Put 2 shitake mushrooms in each bowl. Set on saute function. When the broth is boiling, briefly blanch the green vegetable and additional mushrooms (optional) and divide among the 4 bowls. Taste the broth and adjust the seasoning. Laddle the broth in the bowls of noodles.
Sprinkle the sliced green onion and coriander on top. Serve piping hot with a side dish of pickled green papaya.