Place the carrots, broth and 1 teaspoon of the oil in a large pan and bring to a boil over medium-high heat. Cover, reduce the heat to medium and continue to cook until the carrots are tender, 12 to 14 minutes. Uncover and cook, stirring, until the liquid has evaporated and the carrots are lightly browned, another 2 to 3 minutes. Season with 1/4 teaspoon salt and 1/4 teaspoon pepper.
Meanwhile, combine the mint, parsley, juice, zest and remaining 3 teaspoons oil in a small dish. Sprinkle with salt and pepper. Toss the warm carrots with the herb mixture.