Begin by scrubbing the mussels in cold water and scraping off any barnacles with a knife. Discard the fibrous material between the hinge of any mussel, if apparent. Also, discard any mussels that are not tightly closed, or which fail to close then sharply tapped.
Next, heat a wok or large frying pan over high heat and then add the oil. Stir in the garlic, ginger, chilies, and scallions and stir-fry for about 30 seconds. Then, grate the rind of the limes into the ginger mixture and then squeeze both fruit and add the juice to the pan with the coconut milk, soy sauce, and sugar. Stir to combine.
After bringing the mixture to a boil, add the mussels, and return to a boil. Cover the pan, and cook briskly until the mussels have all opened, roughly 5 to 6 minutes. Discard any mussels that have not opened.
Remove the pan from the heat and stir in the chopped cilantro. Season the mussels well with salt and pepper before ladling then into warmed bowls. Serve immediately.