Wash the mussels under cold running water and discard any open ones that do not close when tapped.
Remove the fibrous beards and barnacles from the mussels and rinse again.
Fry shallots in olive oil over low heat until soft then add garlic, ginger, chillies, lime leaves, sugar, and lemongrass.
Gently cook the aromatics for eight minutes using a little water if the mixture begins to colour.
Pour in fish stock and simmer until reduced by half then stir in coconut milk and simmer for five more minutes.
Season the broth with soy sauce and lime juice to taste and allow to cool.
Cook mussels in a covered pan over medium heat until all shells have opened.
Discard any mussels that remain closed and pour the prepared broth over the open mussels.
Rub sliced sourdough with olive oil and chargrill both sides on a griddle pan.
Garnish with basil, coriander, and lime zest before serving in bowls with the bread.