1. In a large saucepan of boiling water, blanch the carrots for 1 minute. Drain and let cool, then pack the carrots into a 1-quart heatproof jar. Add the mint.
2. In a small skillet, toast the cumin seeds over moderate heat, stirring, until fragrant, about 40 seconds. Let cool, then add to the jar. In a saucepan, bring the vinegar, water, garlic, salt and sugar to a boil. Simmer over moderately high heat until the salt and sugar dissolve. Ladle the pickling liquid into the jar; if necessary, add more vinegar to cover the carrots. Let the pickles cool, then cover with a lid and refrigerate until flavorful, about 3 weeks.