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Place the cured duck in a large sous vide bag with the duck fat. Seal at 100 percent and sous vide the legs at 180.5 degrees F. for 8 hours. Cool the bagged duck in an ice bath and refrigerate.
For the soup base: Heat the coconut cream in a 4-quart pot until boiling. Add the curry paste mixture. Lower the heat to medium, stir the mixture and cook until the curry paste is completely incorporated and the sauce is thick, approximately 15 minutes.
In a separate 2-quart pot, combine the chicken stock, fish sauce, soy sauce and palm sugar and bring to a boil. Add the chicken stock mixture to the coconut cream and curry paste. Cook at a low boil until thickened, about 20 minutes.
For the squid ink pasta: Pour the flour on a work table and make a well in the middle. Combine the eggs, gochugaru and squid ink together in a small bowl and pour into the well. Add salt and slowly whisk together the eggs and flour with a fork, collapsing the flour wall slowly into the eggs. Incorporate all the egg mixture into the flour and knead for 10 minutes. Form the dough into a flat disc and wrap it in plastic. Let it rest 1 hour before rolling it out with a pasta machine to fettuccine width.
For garnish and assembly: Preheat the oven to 450 degrees F. Reheat the soup to a simmer.
Heat an 8-inch saute pan over medium heat, add some grapeseed oil and, working in batches if necessary, sear the duck legs until the skin crisps up, about 2 minutes per side. Transfer the pieces to a baking sheet and place in the oven until heated through, about 5 minutes. Remove from the oven and let rest, keeping the duck warm.
Cook the pasta in boiling salted water for 1 to 2 minutes. Drain and divide among 6 deep soup bowls. Pour the soup in the bowls, top with the duck confit. Garnish with the cilantro, lime, gyoza strips and cabbage and drizzle in the coconut milk.