Recipe adapted from original by Mary Karlin & Elaine Johnson published in Sunset, Feb 2014
Sterilize your jar and other equipment by rinsing in a solution of 1 Tbsp. bleach + 2 quarts of water, then a rinse of plain water. Air dry.
Put ginger and mint in the clean jar and bruise with a muddler, or wooden spoon until very fragrant. Add pineapple and enough vinegar to cover the fruit. Close the jar tightly and shake vigorously for 10 seconds. Push down the fruit if they have floated up to the top - you want everything completely covered with vinegar so you don't grow any mold or other undesirable bacteria.
Replace the lid with a piece of cheesecloth, and secure it to the top of the jar using a rubber band. Leave out at room temperature for 12 hours.
Discard cheesecloth, replace the lid, secure tightly, and shake daily for 3 days, keeping at room temperature.
On day 4, you want to discard the mint. Do this by pouring everything into a strainer set over a bowl. Return everything except the mint to the jar and shake well each day for 4 more days at room temperature.
After 7 days, strain out the solids and return liquid to the jar. Add lime juice and sugar, cover, and shake until sugar is dissolved. Add the mint sprig and set in refrigerator for 7 days, shaking the jar every day to make sure sugar is dissolved.
Discard the mint and chill for up to 4 months. Use a few tablespoons in each drink, mixing with sparkling water (or see original article for cocktail and marinade ideas).