Bring the vinegar, 2 cups water, the palm sugar, fish sauce and kosher salt to a boil in a nonreactive saucepan. Once the mixture is at a full boil, add the long beans, garlic, chiles, kaffir lime leaves and galangal. Stir to combine and boil for 1 minute. Turn off the heat and cool completely.
Put the cooled beans and brine into a large bowl, cover with plastic wrap and refrigerate for at least 24 hours before serving.
Cook's Notes: The pickled long beans are a great accompaniment to sandwiches, in salads or eaten on their own. The brine can be used to make vinaigrettes or added to dishes that might need a touch of acid.
Galangal can be found at Asian markets; however, you may substitute an equal amount of fresh ginger if you cannot find it fresh.