How to Make It
In a large stockpot, bring 5 quarts of water to a boil. Add 1 tablespoon of salt and the chicken, breast side down. Place a heatproof plate over the chicken to keep it submerged and bring to a boil. Reduce the heat and simmer the chicken for 30 minutes; it will not be cooked through. Transfer the chicken to a bowl of ice water and let cool completely. Drain well and pat dry.
Meanwhile, in a large cast-iron skillet, combine the star anise, cardamom, coriander, cinnamon stick, black and white peppercorns and goji berries. Cook over moderately low heat, stirring, until very fragrant, about 3 minutes. Transfer to a small bowl.
In the same skillet, combine the shallots, onion and leek. Cook over moderate heat, stirring occasionally, until deep golden, about 10 minutes.
Remove all of the meat from the chicken and coarsely shred it.
Return all of the chicken skin and bones to the broth in the stockpot. Add the pan-roasted shallot, onion and leek mixture and bring to a boil. Cover and simmer over moderately low heat for 1 hour.
Stir the toasted spices and goji berries into the broth. Cover and simmer for 1 hour longer. Add the rock sugar and simmer for another 30 minutes.
Strain the broth into a large bowl, pressing on the solids; discard the solids. Pour the broth into a clean saucepan.
Prepare the garnishes: Soak the noodles in a large bowl of boiling water until pliable, 8 to 10 minutes.
In a large skillet, heat the oil. Add the shallots and cook over moderate heat, stirring, until golden brown, 5 to 7 minutes. Using a mesh skimmer, transfer the shallots to a paper towel–lined plate to drain. Let cool.
Bring the broth to a simmer. Stir in the shredded chicken and cook until just white throughout, 1 to 2 minutes. Stir in the fish sauce and season the broth with salt.
Drain the rice noodles and transfer to large bowls. Ladle the broth and chicken over the noodles. Top with the scallions and cilantro. Garnish with the crispy shallots, bean sprouts, basil, mint and jalapeños and serve with lime wedges.