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 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.