1. Bring a medium pot of water to a boil. Add salt to boiling water, then add cabbage; cook until crisp-tender, about 2 minutes. With a slotted spoon, transfer greens to a colander to drain.

2. Bring stock to a simmer in a large saucepan over medium-high heat, and add mussels. Cover pan, and cook until mussels open (check pan frequently after 2 minutes). With a slotted spoon, transfer mussels as they open to four large soup bowls, dividing evenly. (Discard any mussels that remain unopened after 5 minutes.) Divide reserved greens among the soup bowls.

3. Pour broth from pan through a fine sieve into a bowl, and rinse pan. Return broth to pan, and stir in green-curry paste. Bring to a simmer over high heat. Add coconut milk, whisking until incorporated. Bring to a bare simmer.

4. Divide broth among bowls, pouring over mussels and greens to reheat. Serve with lime wedges. Garnish with garlic chives, if desired.