At least 24 to 36 hours before serving
Mix together the salt and sugar in a bowl. In a separate bowl mix together the remaining spices then coat the dug legs with them. Place the duck legs in a plastic bag or non-reactive container and pack the salt and sugar cure evenly around them. Refrigerate for 8 to 12 hours.
Preheat a water bath to 167°F (75°C).
Wash the cure off of the duck legs then place into a sous vide bag and seal. Cook the duck for 16 to 24 hours.
Once cooked, remove the duck from the sous vide bag and pat dry. Sear the duck legs in a hot pan until crispy. Remove the meat from the bones and shred.
40 minutes before serving
Bring a pot of water to a boil and then add the noodles. Cook until tender but still slightly firm. Drain the noodles.
Blend together the sesame oil, soy sauce, rice wine vinegar, sesame paste, peanut butter, and brown sugar. Stir in the chile-garlic paste, garlic, scallions, sesame seeds, and ginger. Toss the noodles with the sauce. If serving cold you can let them cool and then refrigerate them at this point.
Place a pile of noodles on a plate or in a bowl. Top with the cucumber, carrots, and sprouts. Add the peanuts then the shredded duck. Sprinkle with the cilantro and sesame seeds, then serve.
Because xanthan gum is a modernist ingredient, the amounts for this component are given in metric by weight. Learn more about how to measure modernist ingredients in this article.
I usually add 0.15% xanthan gum when I blend together the oil, soy sauce and rice wine vinegar for the noodle sauce. This helps with the mouthfeel of the sauce and it clings to the noodles better.