Peel the eggplants & cut them into 1/4" thick slices. Bring the vinegar, water & salt to a boil in a heavy saucepan.
In the boiling liquid, immerse as many of the eggplant slices as possible in one layer.
Lower the heat to a simmer & set a weighted plate on top of the eggplant to keep it submerged. Cook for about 10 minutes, until it is soft & easily pierced.
Remove with a slotted spoon. Repeat with the remaining slices of eggplant. If the liquid becomes too concentrated, add 1 c more of both water & vinegar.
Arrange a layer of eggplant slices in a glass bowl. Sprinkle with some mint, garlic & red pepper flakes. Repeat until all the layers are used up & cover with olive oil. Cover & allow to marinate at room temperature for 2 days.
Serve as part of an antipasto or with any salad.
VARIATION: Melanzane Sott''Olio II: A stronger version. Cut the peeled eggplant into 1 1/2" thick slices. Bring 4 c red wine vinegar, 2 c water & 1 tb coarse sea salt to a boil. Cook submerged eggplant for 5 minutes; it should be just piercable by a knife but not soft. Drain well & proceed as above.