Preheat oven to 375°F. Whisk juice, 1 tablespoon oil, and vinegar in small bowl to blend; set aside.
Stir remaining 1 tablespoon oil, crushed red pepper, and salt in medium bowl. Add carrots and toss to coat. Scrape carrot mixture onto large rimmed baking sheet. Arrange carrots in single layer.
Roast carrots until almost tender, stirring occasionally, about 15 minutes (depending on size). Add juice mixture and toss to blend. Roast until juices are reduced to glaze and coat carrots, stirring occasionally, about 10 minutes longer. Season to taste with more salt, if desired. Transfer carrots to large bowl; add mint and orange peel and toss to blend. Transfer to serving bowl.
