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Combine the coconut milk, lemongrass, basil, brown sugar, fish sauce, and ginger in a heavy-bottomed saucepan.
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Bring to a boil, stirring until the sugar dissolves, then reduce to a simmer.
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Place the curry paste in a small bowl. Ladle in a bit of the hot coconut milk mixture in whisk it with a fork until it dissolves.
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Add the liquid to the pot and simmer until it is reduced by 3/4. (about 20 minutes)
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At about the 15 minute mark, place a steamer in large pot. Add the sake and bring to a boil. About 1-2 minutes)
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Examine the mussels and throw out any that may have opened. Throw the rest in the pot and steam until they have opened (about 5-7 minutes.)