Stand the carrots upright in six hot, sterilized pint canning jars. Add a sprig of dill or lovage to each jar. Divide up the peppercorns, mustard seeds, and garlic; sprinkle equal amounts into each jar. Boil together the vinegar, water, and honey or sugar until the sugar dissolves. Pour the hot liquid over the carrots, covering them completely. Seal and refrigerate for at least 1 week before using. The carrots will keep for at least a month, refrigerated.