Heat oil in large skillet over medium-high heat until shimmering. Cook carrots and parsnips, stirring occasionally, until golden brown, 12 to 14 minutes.
Whisk orange juice, honey and 1 teaspoon salt in small bowl until blended. Add mixture to skillet and cook covered, stirring occasionally, over medium-low heat until vegetables are tender and liquid has evaporated, 12 to 14 minutes. Stir in herbs and season with salt and pepper.