Heat a large skillet over medium heat; add coconut oil. When oil is hot, add shallot and fry them until lightly golden, about 2 to 3 minutes. Remove fried shallot from skillet and place on a paper towel lined dish and set aside.
In same skillet with shallot infused coconut oil; add garlic, lemon and chili. Sauté until they are soften, about 2 to 3 minutes. Add mussels, water, rice wine and fish sauce. Increase heat to high heat and stir to combine everything. Cover and cook until muscles are fully cooked, about 6 to 8 minutes. Discarded un-opened mussels.
Reduce heat to medium; sprinkle basil and pour coconut milk cook additional 1 minute. Add black pepper to taste, and remove from heat. serve with lime and toasted crusty bread. Enjoy!