Place a soup pot over medium-high heat. Pour 500 ml of water into the pot and add the crushed galangal, garlic, and kaffir lime leaves. Bring the water to a boil, then let the herbs simmer for about 5 minutes until fragrant.
Add the chicken legs to the herb-infused soup and keep the heat at a steady simmer. Stir in the fish sauce, sweet dark soy sauce, and palm sugar, ensuring the flavors blend well.
Next, add the salt and ground black pepper. Let the chicken simmer gently for about 20-30 minutes, allowing the flavors to meld and the chicken to become tender.
Once the chicken is cooked and tender, taste the broth and adjust the seasoning to your liking. The flavors should be a perfect blend between sweetness and saltiness. Then, reduce the heat to low.