Rinse the whole chicken and pat dry. Stuff the bruised thumb-sized ginger and the trimmed scallions into the cavity. Rub 2 teaspoons of salt all over the chicken to smooth the skin.
In a stockpot large enough for the chicken, bring the 10 bowls (≈3 L) of chicken stock and the remaining 1 teaspoon of salt to a boil.
Submerge the chicken breast-side down in the boiling stock, then immediately reduce to a gentle simmer and poach for 35–45 minutes, depending on size, until cooked through.
Remove the chicken and plunge it into the ice-cold water bath for 10 minutes. Reserve and strain the poaching broth for cooking the rice and sauce. Discard the ginger and scallions from the cavity, then drain and set the chicken aside to cool before chopping into serving pieces.
Heat 5 tablespoons vegetable oil in a wok over medium heat. Fry the finely minced shallots (4 cloves worth) and 4 cloves minced garlic until fragrant and golden.
Add the 3 cups washed rice to the wok and stir to coat the rice with the flavored oil and aromatics, then transfer the rice mixture to the rice cooker.
To the rice in the cooker add 2.5 cups plus 2 tablespoons chicken broth, the bruised small ginger, 1 tablespoon garlic and shallot oil, 70 g chicken fat, and 1.5 teaspoons salt. Stir gently, then cook the rice according to your rice cooker instructions.
Make the soy drizzle by combining 2 teaspoons light soy sauce, 2 teaspoons chicken broth, 3 teaspoons sesame oil, and 3 teaspoons garlic and shallot oil. Stir and set aside.
Prepare the chili-garlic sauce: mix 3 tablespoons Huy Fong chili garlic sauce, 15 g grated garlic, 50 g grated ginger, 1 teaspoon salt, 1 teaspoon sugar, 3 tablespoons chicken broth, and 1 tablespoon lime juice. Taste and adjust salt, sugar, or lime juice as needed.
To serve, line a platter with cucumber rounds, place rice and the chopped chicken pieces on the plate, drizzle some of the soy mixture over the chicken, garnish with cilantro sprigs, and serve with the chili sauce and a bowl of the reserved chicken broth on the side.