Trim the tops of the carrots. Scrub the carrots well but do not peel; halve lengthwise. Wash the chopped leeks thoroughly.
Melt the butter in a wide pot over medium heat. Add the leeks and 1/4 teaspoon salt and toss to coat. Cover and cook, stirring occasionally, until almost tender, about 8 minutes. Add the carrots, lemon zest, nutmeg, 1/2 teaspoon salt, 1/4 teaspoon pepper and 1/2 cup water. Cover and continue cooking, stirring occasionally, until the carrots are tender, 15 to 20 more minutes.
Add half of the herbs, the lemon juice, and salt and pepper to taste; toss. Transfer the vegetables to a platter and top with the remaining herbs.