Combine the cinnamon, shallots, lemongrass, cilantro stems, garlic and ginger in a large bowl. Finely grate the zest of the limes into the bowl (reserve the limes separately) and stir in the coconut milk. Reserve 1 1/2 cups of the coconut mixture separately, then add the chicken wings to the bowl with the remainder and toss to coat. Cover the bowl with plastic wrap and refrigerate for at least 2 hours, or preferably overnight.
Meanwhile, make the pickle: Combine the shallots, cucumber, carrot and 1 tablespoon salt in a medium bowl. Carefully pour 3 cups boiling water over the vegetables, then stir to mix evenly and let stand for 20 minutes. Drain the vegetables in a colander, pressing gently to remove excess liquid, then transfer to a bowl. Add the vinegar, sugar, chile and 1 teaspoon salt, stirring to dissolve the sugar and salt. Refrigerate until ready to use, at least 10 minutes and up to 1 hour.
Bring 4 cups water to a boil in a large pot. Add the wings with their marinade, return to a boil, then reduce the heat to maintain a steady simmer. Cook, stirring occasionally, until a paring knife inserted in the middle of a wing comes out with no resistance, about 15 minutes. Using tongs, transfer the wings to a wire rack set over a rimmed baking sheet, season liberally with salt and let air-dry while you make the dipping sauce.
For the dipping sauce: Place the reserved 1 1/2 cups aromatics and coconut milk in a medium sauce pan over medium heat; stir in 1 cup water and bring to a simmer. Cook, stirring occasionally, until reduced and thickened, about 20 minutes. Transfer the sauce to a blender, along with three-quarters of the cilantro leaves and the juice of the reserved limes; puree until smooth. Pour the coconut dipping sauce into a bowl, season with salt and pepper and let cool completely.
Heat 2 inches of oil in a large, heavy-bottomed pot over medium heat until a deep-fry thermometer registers 425 degrees F. Working in 2 batches, fry the wings, turning occasionally, until golden brown and crisp, about 2 minutes per batch. Transfer the wings with a slotted spoon to a clean rack set over a baking sheet and season with more salt. (Make sure the oil returns to the proper temperature between batches.)
Transfer the wings to a serving platter and sprinkle with cilantro. Serve immediately with coconut dipping sauce and cucumber and carrot pickles.
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