Peel carrots. Ribbon 1 carrot with a vegetable peeler, and transfer to a bowl. Toss ribbons with 1 teaspoon rice wine vinegar and 1 teaspoon sesame seeds, for garnish; set aside.
Cut remaining carrots crosswise into 1-inch pieces, and add to a medium saucepan with 2 inches of water to cover. Bring water to a boil, and simmer carrots 15 minutes. Add garlic cloves, and simmer 5 minutes more or until carrots are very tender.
Using a slotted spoon, transfer carrots and garlic to a food processor. Purée carrots and garlic, 3 cups cooking water, and ginger until smooth. Transfer to a saucepan, and stir in remaining 1 teaspoon vinegar and sesame oil. Bring soup to simmer.
Ladle soup into 4 bowls, and garnish with carrot ribbons and remaining 2 teaspoons sesame seeds.
Time-saver alert! Make a double batch of this soup and freeze in an airtight container for up to three months. Just thaw, heat, and serve for a last-minute dinner.