Heat the oil in a large saucepan over medium-high heat. Add curry paste and fry, stirring occasionally, for 5 minutes or until slightly darkened and fragrant.
Add coconut milk and simmer for 3-4 minutes until slightly thickened. Strain into a jug, discarding solids.
Return liquid to the pan and place over high heat.
Add mussels and kaffir lime leaves, then cover and cook for 3-4 minutes until the mussels have just opened. Add fish sauce, sugar and lime juice and season with salt.
Divide curry among bowls, scatter over coriander and serve with lime wedges.
