Pour the white vinegar and the water into an 8-quart pot. Cover and bring to a simmer over high heat. Lower the heat to the warm setting and keep warm while you proceed with the recipe.
Peel the eggplants and trim the ends. Cut each eggplant in half lengthwise. Slice one half into ¼-inch slices, then stack and slice widthwise into ⅛-inch strips. Place the strips in a bowl and sprinkle with a generous amount of salt and toss well to mix. Repeat the process of slicing, salting, and tossing until all the eggplant has been sliced. It will seem like you’re using a lot of salt, and you are, but you need it for the eggplant to release its moisture, and the vinegar bath will remove any overly salty taste.
By the time you finish slicing the eggplant, it will have released a lot of dark liquid. Set a colander in the sink. Raise the heat under the pot of vinegar to medium and bring it to a simmer. You’ll be working quickly for the next few minutes, so avoid any distractions or you’ll overcook the eggplant and make it mushy. Remove the cover from the pot and pick up ahandful of the eggplant. Using both hands, squeeze as much liquid out of the eggplant as you can, letting the dark juices fall back into the bowl. Carefully lower the eggplant into the simmering vinegar. Continue quickly squeezing handfuls of the eggplant, then adding them to the vinegar. Stir the eggplant with a slotted spoon. Immediately after adding the last of the eggplant, carefully drain the eggplant into the colander you’ve set in the sink. Squeeze out as much liquid as you can. I place a cover from a small pot on the eggplant, then use my hands to press on it to squeeze out the excess vinegar bath.
Turn the eggplant into a bowl. Add ⅓cup of olive oil and the garlic, peppers, oregano, and alittle black pepper. Toss well to combine. Taste for seasonings. Pack the eggplant mixture into the clean glass jars, stopping 1 inch from the top. Add olive oil to fill the jars completely. Cover and tighten the lids on the jars. Label the jars and add the date. Set aside in a cool, dry place (unrefrigerated) for 5 days.
Open the jars every day and add olive oil as needed to fill the jars as the eggplant absorbs some of the oil. Cover tightly after checking each day. After 5 days, store in the refrigerator for up to 5 months.