Cider vinegar gives these carrots the flavor of an apple cider reduction, but in a fraction of the time. To get a head start, boil the carrots a day ahead. Refrigerate them in a zip-top plastic bag, then sauté just before serving.
Place carrot in a large saucepan; cover with water. Bring to a boil. Reduce heat; simmer 1 minute or until tender. Drain.
Combine brown sugar and remaining ingredients except parsley in a large nonstick skillet over low heat; cook until butter melts, stirring frequently. Bring to a boil.
Reduce heat to medium; add carrots. Cook 3 minutes or until carrots are glazed and thoroughly heated, stirring constantly. Sprinkle with chopped parsley; toss to combine.
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