1. In a wok or large pot, combine 1 cup of the coconut milk with the galangal, lemongrass, and lime leaves and bring to a boil. Add the chicken, fish sauce, and sugar, reduce the heat to medium, and simmer until the chicken is white and firm, about 4 minutes. Add the remaining coconut milk and heat to just below boiling, about 3 minutes.
2. Divide the lime juice and curry paste into individual serving bowls and ladle the soup over them. Garnish each bowl with the cilantro and crushed chile peppers. Serve immediately.
Heat oil in a large heavy pot over medium heat. Add curry paste and cook, stirring, until fragrant, about 1 minute. Add carrots, onion, and pepper and cook, stirring occasionally, until onion is translucent, about 10 minutes.
Add potatoes, chicken, coconut milk, and 1 1/2 cups water and bring to a boil. Reduce heat to a simmer and cook, stirring occasionally, until chicken is cooked through and potatoes are tender, about 20 minutes. Divide curry among bowls and top with herbs.
