This salad a favorite at Tra Vigne is all about contrasts. The acidity of the raw onion, the brininess of the olives, and the hot, crispy sweet onions give you a little bit of everything in each bite.
In a large nonreactive bowl, toss together the 2-1/2 cups onions, vinegar, salt to taste, olives, lemon slices, and olive oil. Set aside.
Heat the peanut oil in a deep fryer or deep pot to 350°F. Meanwhile, put the buttermilk in a bowl. Working in small batches, toss the onion rounds in the buttermilk. Put them in a sieve to shake off the excess liquid. Holding the sieve over another bowl, pour the fritti flour or rice coating over the onions. Toss to coat well and shake off the excess.
Drop a single piece in the oil to test the heat. If it rises immediately to the surface, the oil is ready. Fry the onion rounds in small batches until crispy, about 2 minutes. Scoop out with a slotted spoon and drain on paper towels. Put in a low oven to keep warm.
To serve, using a slotted spoon, remove the marinated onions from the marinade and divide among salad plates. Pile the crispy onions on top. For a pretty presentation, tuck the lemon slices and olives from the marinated onions throughout each portion. Dust each with mint and serve.
Chef's Note: If you prefer a slightly tarter flavor, cut back on the oil in the marinated onions. Be sure to use a sharp chef's knife or a mandoline to cut thin slices of the onion and the lemon.