Heat 2 tablespoons of the oil in a large skillet set over medium-high heat. Add the garlic and ginger and cook, stirring, until slightly softened and fragrant, about 2 minutes. Add the carrots, 2 1/2 cups water, vinegar, soy sauce, brown sugar, curry powder and 1 teaspoon salt. Bring to a simmer, cover and cook until the carrots are tender, about 15 minutes. Let the mixture cool. Transfer the mixture to a blender and add the remaining 1 tablespoon oil. Keep the sauce at room temperature.
Meanwhile, bring a large pot of salted water to a boil and cook the pasta according to the package directions. Drain, toss with some oil and cool to room temperature. Add the carrot-ginger sauce, chicken, scallions and some salt. Add some hot water to thin out the sauce if necessary. The noodles should be fairly loose and slippery, as the pasta will absorb much of the sauce once it is refrigerated. Refrigerate in an airtight container for up to 3 days.
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