Step 1

In a large stockpot, bring water to a boil. Stir in the salt, then add the chicken bones, whole chicken, breast side down. If the chicken floats up above the water, place a heatproof plate over the chicken to keep it submerged. Return water to a boil then reduce the heat and simmer the chicken for 30 minutes, skimming off any foam that collects at the surface. Using tongs, carefully remove the plate from the stockpot. Transfer the whole chicken to a bowl of ice water and let cool; it will not be completely cooked through. Do not discard the broth in the stockpot.

Step 2

While chicken is cooling, prepare the seasonings for the broth. In a large cast-iron skillet, combine the star anise, cardamom pods, fennel seeds, black peppercorns, and cinnamon stick. Cook the spices over moderately low heat, stirring occasionally, until very fragrant, about 3 minutes. Add spices to broth in stockpot.

Step 3

In the same skillet, add the shallots and onion. Cook over moderate heat, stirring occasionally, until deep golden brown on all sides, about 10 minutes. Add onion and shallots to the stockpot.

Step 4

Remove all of the meat from the chicken and coarsely shred it. Refrigerate the shredded chicken until ready to serve.

Step 5

Return all of the chicken skin and bones to the broth in the stockpot and bring broth to a boil. Cover partially and simmer over moderately low heat for 2 hours. Add the brown sugar and simmer for another 30 minutes.

Step 6

Strain the broth through a fine mesh strainer into a large saucepan, pressing on the solids; discard the solids.

Step 7

Cook the noodles in a large saucepan of boiling water until pliable, 5 to 8 minutes. Drain the noodles and rinse well. Divide the noodles among serving bowls.

Step 8

Bring the broth to a simmer. Stir in the shredded chicken and cook until just cooked through, 1 to 2 minutes. Taste the broth and season with salt as needed.

Step 9

Ladle the hot broth and chicken over the noodles. Top with cilantro and a squeeze of lime. Add other garnishes as desired.