In a large pot with a lid, bring the rice and 4 quarts (16 cups) water to a boil. Add the chicken (including wings and legs), lemongrass, ginger and 1 tsp. salt. Simmer, partially covered, over medium until the chicken is cooked through, about 25 minutes. Transfer the chicken to a large bowl. Let cool, then shred the chicken, discarding the skin and bones.
Meanwhile, continue cooking the rice, uncovered, over medium-high, stirring occasionally, until the rice breaks down and the soup is thick and creamy, 20 to 25 minutes. Stir in the fish sauce; season with salt. Discard the lemongrass and ginger.
In a small saucepan, heat the canola oil over medium-high. Fry the garlic, stirring often, until just golden, about 1 minute; transfer to paper towels.
Divide the soup among 4 bowls. Drizzle with the sesame oil. Top with the chicken, cilantro, chile and fried garlic.