David Lebovitz and the Food Network both offer recipes for pickled jalapeños made with vinegar. The David Lebovitz recipe includes carrot, dried oregano and bay leaf, whereas the Food Network recipe does not. Find the recipes at DavidLebovitz.com and FoodNetwork.com, respectively.
For David Lebovitz's recipe, make a pickling brine by heating 1 cup of white or unseasoned rice vinegar with 1 cup of water, 1 garlic clove, 1/2 teaspoon of dried oregano, 10 crushed black peppercorns and 1 bay leaf in a saucepan. Stir in kosher or sea salt and sugar until they dissolve in the liquid. Add eight 1/4-inch-sliced jalapenos, 1 medium 1/4-inch-sliced carrot and 1/2 sliced red onion to the brine to simmer for a minute. Allow the pickle mixture to cool, then transfer the mixture to jars, fasten the lids, and set them in the refrigerator until ready to serve.
While David Lebovitz's pickled jalapenos last about one month, The Food Network's recipe involves a canning process that extends the shelf life of the pickles to up to one year. Make the brine by adding 2 cups of white vinegar, 2 cups of filtered water, 2 tablespoons of pickling salt, 2 cloves of garlic, 1 tablespoon of whole black peppercorns, and 1 tablespoon of honey or sugar to a saucepan, and simmer over medium heat. Add 1 pound of sliced jalapeno peppers, and bring to a boil. Transfer the mixture to sterilized jars, fasten the lids, and then process in a canner for five minutes.
Remove the jars from the canner, and allow them to rest on a cooling rack for 12 hours before consuming.