To make the green sauce, put the cilantro, basil, mint, ginger, garlic, chiles, coconut, lemongrass, fish sauce, sugar, and salt in a blender or food processor. Quickly process to make a smooth, thick puree, adding a little ice water if necessary. Taste and adjust the seasoning; it should be quite spicy.
Season the fish chunks lightly with salt and pepper. Heat the oil in a wide deep pan over medium heat. Add the fish and fry lightly for 1 minute on one side. Flip the fish and raise the heat to medium-high. Add the broth and half of the green sauce, then put on the lid and cook for 2 minutes, or just until the fish is opaque throughout. Gently stir in the remaining green sauce. Taste the broth and adjust the salt if necessary. Ladle the stew into bowls, sprinkle with the scallions, and serve with lime wedges.