In a large stockpot, add the coconut milk, fresh lime juice, white wine, Thai red curry paste, minced garlic, fish sauce, and white sugar.
Heat over medium heat, stirring until the sugar and the curry paste are dissolved. Then bring to a boil and simmer for 2 minutes.
Add the mussels, cover the pot, and continue to boil and steam the mussels for 5 – 8 minutes, stirring occasionally until the mussels are opened.
Remove from the heat and discard any mussels that did not open.
You can carefully transfer the mussels and sauce into a large serving dish or spoon into individual serving bowls.
Sprinkle with a few pinches of finishing Kosher salt and generously sprinkle the chopped cilantro and green onion if used.
Serve with sliced baguette; enjoy!