Place mussels in a pan of cold water. Discard any that float. Drain, clean, and debeard remaining mussels.
Place stock and lemongrass in a saucepan over medium heat; bring to a boil. Add mussels and let steam, covered, until they open, 1 to 4 minutes. Discard any mussels that do not open.
Transfer mussels to a bowl and sprinkle basil on top. Serve with another bowl alongside for discarded shells.
