Heat a large pot over medium heat and add the shallots, garlic, and chilies. Cook until the shallots soften.
Add the galangal slices and bruised lemongrass stalks. Stir for one minute to release their aroma.
Pour in both cans of coconut milk and add the kaffir lime leaves. Bring the mixture to a gentle simmer.
Stir in the fish sauce and palm sugar until the sugar dissolves.
Add the fish pieces and simmer for 6 to 8 minutes until the fish turns opaque and flakes easily.
Remove the pot from heat and stir in the lime juice. Discard the galangal, lemongrass, and kaffir lime leaves if desired.
Ladle the stew into bowls and top with fresh cilantro leaves.