1. Preheat broiler to high.
2. Place chile on a foil-lined baking sheet; broil 3 inches from heat for 8 minutes or until blackened and charred, turning after 6 minutes. Place in a paper bag; fold to close tightly. Let stand 10 minutes. Peel, and discard skins. Chop chile.
3. Combine chopped chile, wine, shallots, 3 tablespoons cilantro, salt, and next 4 ingredients (through clam juice) in a Dutch oven; bring to a boil. Cover, reduce heat, and simmer 8 minutes. Add mussels; cover and cook 3 minutes or until shells open. Remove mussels from pan with a slotted spoon. Discard unopened shells. Keep warm.
4. Bring wine mixture to a boil over high heat; cook until mixture is reduced to 1 cup. Stir in lime juice and butter. Pour liquid over mussels; toss gently. Sprinkle with remaining 1 tablespoon cilantro. Serve immediately.
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