In a small saucepan, combine the pomegranate vinegar, water, honey, and salt. Bring to a simmer, stirring until the honey and salt dissolve.

Place the carrot sticks, peppercorns, coriander seeds, and garlic in a clean quart-size jar.

Pour the hot pickling liquid over the carrots. Let cool to room temperature, then cover and refrigerate.

The carrots are ready after about 4 hours but are best after 24 hours. They will keep refrigerated for up to 3 weeks.