Heat oil in a large saucepan over medium heat.
Add lemongrass and ginger and cook, stirring frequently, until slightly caramelized and fragrant, about 1 minute.
Carefully stream in the seafood stock and coconut milk. Cover, reduce the heat to low, and cook, stirring occasionally, for 30 minutes.
Strain the broth into a 4-cup liquid measuring cup, discarding the ginger and lemongrass.
