In a pan of cold water, throw in the mussels. Discard any that float.
Clean and debeard the remaining mussels.
In a pan, bring the lemongrass and the stock to a boil, then add the mussels and steam, covered, until they open (discard any that do not open). Can take as little as 30 seconds, or as much as 4 minutes.
Sprinkle with the basil.
Serve in 2 dishes, one to eat from, one to take the discarded shells.