Peel carrots and cut into 1/4-in. matchsticks.
Bring 3 cups water and all ingredients except carrots to a boil in a large saucepan. Reduce heat to low and simmer 1 minute. Add carrots and simmer until almost tender, 2 to 3 minutes.
Transfer carrots and liquid to a bowl and let cool to room temperature. Chill, covered, overnight to let flavors develop. Serve cold. Keeps, chilled, up to 1 week.
Note: Nutritional analysis is per 1/4-cup serving.