Bring water to a simmer in a large saucepan. Stir in carrots and next 8 ingredients (carrots through garlic); cover and simmer 15 minutes or until carrots are tender. Remove carrots with a slotted spoon, reserving liquid.
Bring liquid to a boil; cook until reduced to 1/4 cup (about 10 minutes). Discard mint sprig and cinnamon stick. Return carrots to pan; stir in olives, vinegar, and oil. Cook 1 minute or until heated. Sprinkle with chopped mint. Garnish with mint sprigs, if desired.