In a large pot, heat oil over medium heat. Stir in onion until fragrant, about a minute. Then add garlic and sauté for 2 minutes.
Add yellow curry paste and cook for 2 minutes. Then add fish sauce. Reduce heat to medium and add mussels. Mix well with the curry mixture. Then add coconut milk, water, and rock sugar. Simmer until the mussels open, add lime juice and serve with basil leaves.