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1
Preheat the oven to 325F.
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2
Put the potatoes in a large saucepan with cold salted water to cover and bring to a boil over high heat.
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3
Cook until tender, about 10 minutes.
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4
Drain well, scatter on a baking sheet, and let cool for several minutes.
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5
Place in the oven to dry out, about 5 minutes.
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6
Let cool, then press through a ricer, the large holes of a box grater, or a colander.
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7
While the potatoes are in the oven, cut the onion half into quarters and slice thinly to yield slim pieces about 1 inch long.
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8
Put in a nonreactive bowl with the vinegar and oregano and let rest for 15 minutes.
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9
Season the potatoes with salt and pepper, then divide into 8 equal balls.
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10
Place a ball in the palm of your hand, top with a piece of cheese, and then a second potato ball.
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11
Shape the potato around the cheese to form a 4-inch patty.
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12
Repeat with the remaining potato balls and cheese.
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13
(The recipe may be prepared to this point, covered, and refrigerated up to 1 day before cooking.)
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14
Heat the 2 tablespoons olive oil in a nonstick skillet over medium heat or in an electric frying skillet set at 350F.
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15
Add the polpette and cook, turning once, until brown and crispy on both sides, about 10 minutes total.
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16
While the polpette are cooking, finish making the salad.
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17
Whisk the remaining 1/2 cup olive oil and salt and pepper to taste into the onion-vinegar mixture.
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18
Add the cucumber, avocados, and tomato and toss well.
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19
Arrange a nest of lettuce on each of 4-plates.
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20
Spoon the salad over each nest.
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21
Top with a polpette and spoon more dressing over all.
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22
Serve at once.
