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Heat oil in large skillet over medium-high heat.
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Add carrots and parsnips.
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Sprinkle with coarse kosher salt and pepper.
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Sauté until vegetables are beginning to brown at edges, about 12 minutes.
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DO AHEAD: Can be made 1 day ahead. Cover and chill.
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Add butter, rosemary, and honey to vegetables.
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Toss over medium heat until heated through and vegetables are glazed, about 5 minutes.
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Season to taste with more salt and pepper, if desired.