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Cook noodles according to package directions. Set aside.
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Heat oil in large skillet over medium heat.
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Add carrot and shallots; cook, stirring frequently, for 3 to 4 minutes.
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Add garlic; cook, stirring frequently, for 1 minute.
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Add ½ cup broth, soy sauce, chicken, cabbage, and bean sprouts; cook, stirring constantly, for 3 to 4 minutes, or until cabbage is tender-crisp. Set aside.
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Divide noodles evenly between 4 serving bowls. Top evenly with remaining broth, carrot mixture, and green onions (if desired).
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Serve immediately.