1. Combine chicken, broth, rice, 1 piece of ginger, white and light-green parts of scallions, 8 cups water, and 1 tablespoon salt in a large pot. Bring to a boil. Reduce heat to low and partially cover. Cook at a bare simmer, stirring a few times, until a meat thermometer inserted into thickest piece of chicken near but not touching the bone registers 160 degrees (the temperature will rise to 165 degrees as chicken rests), 30 to 35 minutes. Transfer chicken to a plate and loosely cover with foil to keep warm.

2. Continue simmering porridge until rice breaks down and mixture is creamy, 45 to 55 minutes more. Remove and discard ginger and scallions. Peel remaining piece of ginger and julienne. Thinly slice scallion tops. Remove skin and bones from chicken, shred meat into bite-size pieces, and stir any accumulated juices from plate into porridge. Place chicken in bottom of serving bowls, spoon over porridge, top with ginger and scallion, drizzle with sesame and chili oils, and season with pepper to serve.