How to Make It
In a medium saucepan, heat 2 tablespoons of the vegetable oil. Add the shallots, celery, carrot, ginger and garlic and cook over moderate heat until softened, about 5 minutes. Add the curry paste and cook, stirring, for 2 minutes. Add the chopped cilantro, basil and mint and cook for 2 minutes; stir in 2 cups of the wine and boil until reduced by three-fourths, about 12 minutes. Add the water and boil until reduced by half, about 10 minutes. Add the coconut milk, brown sugar and lime leaves and boil for 5 minutes. Remove the sauce from the heat and stir in the lime juice and fish sauce. Strain the curry sauce into a bowl.
Meanwhile, in a medium saucepan of boiling water, cook the potatoes until just tender, about 10 minutes. Drain and let cool slightly. Peel the potatoes and cut them in half lengthwise.
Heat 2 tablespoons of the oil in a large nonstick skillet. Add the potatoes, cut side down, and cook over high heat until golden brown, about 5 minutes. Add the butter, season with salt and pepper and cook, stirring occasionally, until golden all over, about 4 minutes longer. Using a slotted spoon, transfer the potatoes to a plate and top with the whole basil leaves; keep warm.
In a large, deep skillet, heat the remaining 2 tablespoons of oil until shimmering. Add the scallions and cook over high heat for 1 minute. Add the remaining 1/4 cup of wine and bring to a boil. Add the curry sauce and bring to a boil. Add the mussels and cook over high heat, stirring occasionally, until they open, 4 to 5 minutes. Discard any mussels that don't open. Spoon the mussels and sauce into deep bowls and serve with the crisp potatoes.
You can substitute two 1-inch strips of lime zest for the kaffir lime leaves.