Bring the stock and 4 cups water to a boil in a medium saucepan over high heat. Add the rice, reduce the heat to medium-low and let simmer while you prepare the aromatics.
Heat 2 tablespoons olive oil in a large saucepan. Add the ginger and garlic and cook over medium heat, stirring, until just starting to brown, 2 to 3 minutes. Stir in the carrots, turmeric and a generous pinch of salt and cook until the carrots glisten and the mixture is very fragrant, about 2 minutes. Add the hot stock mixture and simmer over medium heat until the carrots are tender and the rice is very soft, 8 to 10 minutes.
Meanwhile, heat the remaining 1 tablespoon olive oil in a small skillet. Add the almonds and cook over medium heat, stirring, until lightly browned, 3 to 5 minutes. Transfer the toasted almonds to a plate and season lightly with salt.
Remove and discard the skin and bones of the chicken, then pull the meat into bite-size pieces. Add the chicken, lime juice and fish sauce to the saucepan and cook until warmed through. Stir in 1/2 cup cilantro and season with salt. To serve, ladle the soup into bowls and top with the toasted almonds and the remaining 1/2 cup chopped cilantro.