In a covered large saucepan, cook carrots with salt in a small amount of boiling water for about 3 minutes or until crisp-tender; drain.
Pack carrots into sterilized half-pint canning jars or other jars. Divide fresh ginger among jars; place one of the whole allspice in each jar.
In a small stainless-steel, enamel, or nonstick heavy saucepan, combine the 3/4 water, vinegar, brown sugar, cloves, and peppercorns. Bring to boiling; reduce heat. Simmer, uncovered, for 5 minutes.
Pour hot vinegar mixture over carrots. Wipe jar rims; adjust lids. Cool. Seal and label. Store in the refrigerator for up to 3 months.