Rub the whole chicken inside and out with salt and lime, then rinse thoroughly. Trim excess cavity fat and reserve it for rendering later.
Heat 3 to 4 quarts (3 to 4 L) water to around 120°F (50°C). Lower the chicken into the pot with the breast down and back facing upward to help the meat cook evenly.
Add onion, halved shallots, ginger, salt, and rock sugar. Bring to a gentle simmer, remove foam as it rises, and cook until the chicken is fully cooked. Rest the chicken in the hot broth for about 15 minutes before removing.
Mince the small shallot, slice the large shallot, separate green onion whites and greens, and prepare the mushrooms.
Cook reserved chicken fat over low heat until melted. Reserve about 2 tablespoons of rendered fat for toasting the rice.
Fry sliced shallot in chicken fat until fragrant. Add rinsed rice and toast over medium heat for about 6 minutes until the grains become firmer and slightly opaque.
Check the chicken for doneness, turn off the heat, cover the pot, and allow it to rest in the broth for another 15 minutes.
Transfer chicken briefly to ice water, remove the meat, and shred into bite-size pieces. Return the chicken carcass to the broth to continue extracting flavor.
Add toasted rice to the chicken broth and adjust liquid to about 4 quarts (4 L). Simmer gently for about 30 minutes until the rice softens and blooms. Stir occasionally to prevent sticking.
Heat ½ tablespoon oil, cook minced shallot until fragrant, then add mushrooms, chicken bouillon powder, and water. Cook briefly until seasoned.
Remove the chicken carcass and stir in sautéed mushrooms, chicken bouillon powder, sugar, and optional MSG. Adjust seasoning to taste.
Adjust the porridge texture before serving. Add water or broth if needed because the rice continues absorbing liquid as it cools.
Add green onion whites and black pepper, then ladle into bowls. Finish with shredded chicken, green onion tops, fried shallots, Vietnamese coriander, cilantro, lime, and additional seasonings.
