Wash the eggplants in cold water, remove the stem, cut the eggplants into pieces about 3inches long, and slice these lengthwise as thin as possible: The slices should be less than ¼inch thick.
Wash the peppers, remove their stems, and cut them into 1-inch lengths.
Wash the mint leaves and shake them as dry as possible.
Cover the bottom of the pickling jar with a layer of eggplant, 1 or 2 mint leaves, a piece of pepper, and a bit of garlic. Sprinkle with salt. Repeat the operation, sprinkling salt over each layer of eggplant. As you build up the layers, press them hard toward the bottom of the jar with your fist or fingers. You will soon see that the eggplant begins to shed water.
When you have used up the eggplant and all the other ingredients, place the second jar or tumbler into the pickling jar, putting it in bottom end first. Turn the 2 jars upside down over a bowl and put the weight on top of them. The weight will press the contents of the pickling jar against the bottom of the narrower, taller jar, forcing them to shed their liquid into the bowl. Let stand for 24 hours.
After 24 hours, turn the 2 jars right side up, remove the narrower one, and pour the vinegar over the eggplant. Place the narrower jar inside the pickling jar, turn them upside down again, put the weight on top, and let stand for 12 hours, allowing excess vinegar to run off into the bowl.
After 12 hours, turn the jars right side up, remove the narrower, taller jar, pour enough olive oil over the eggplant to cover amply, and cover the pickling jar tightly. Refrigerate.