Start by cleaning the mussels thoroughly under cold running water. Scrub the shells and remove any beards (the hairy threads) that may be attached. Rinse, scrub, and rinse one more time until water runs clear before beginning next steps.
Pour oil into pan over medium high heat. Add curry paste and cook for 2 minutes.
Add coconut milk, lime juice and zest, with a pinch of salt and pepper. Add mussels and gently stir together. Cover with a lid and cook for 7-12 minutes or until shells open up.
Once shells have opened they are ready, those that do not open should be discarded as they are likely spoiled.
Serve in a bowl with curry sauce from pan over the top with chopped fresh parsley and basil with salt and pepper to taste.