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1
Trim the ends from the eggplants, and shave off some lengthwise strips of the skin with a vegetable peeler, leaving some strips on, creating a striped appearance.
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2
Slice the eggplants lengthwise into 6 or more long wedges, about 1 inch thick.
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3
Peel the red onions, and slice them lengthwise into quarter-round wedges, not cutting at the root; you want the wedges attached.
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4
To poach the eggplants and onions: Put 1 1/2 cups of the vinegar and 2 quarts cold water in the shallow saucepan, and heat to a boil.
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5
Drop in the eggplant wedges and the split-open onions, cover the pan, and return to a boil.
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6
Set the cover ajar, and adjust the heat to maintain a steady gentle boil.
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7
Cook about 30 minutes, occasionally tumbling the vegetables over to poach evenly, until quite soft and tender.
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8
Meanwhile, put the potatoes in another pot, with water to cover them by about 2 inches, and cook just until the potatoes are easily pierced with a fork (dont let them get mushy).
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9
Drain the potatoes, and let them cool briefly.
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10
Peel off the skins, and cut them in half lengthwise, then crosswise into 1/2-inch-thick half-rounds.
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11
Put the potato pieces in the salad bowl, and cover to keep them warm.
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12
When the eggplant and onions are fully cooked, gently lift them out of the poaching liquid with a spider or strainer, and lay them out on a tray or baking sheet in one layer.
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13
While the eggplant is still warm, scoop out the central clumps of seeds from the wedges, then cut them crosswise into 2-inch chunks.
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14
Separate the onion wedges, and then the layers.
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15
Put all the vegetable piecesthey should still be warm to the touchin the bowl with the potatoes.
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16
To dress the salad: Drizzle the olive oil and remaining 2 tablespoons vinegar over the salad, sprinkle the salt on it, scatter in the shredded mint, and crumble the dried oregano over all.
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17
Gently toss the vegetable pieces to coat them all with dressing without breaking them apart.
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18
Serve immediately.
