Shuck the oyster and reserve them separately from the oyster liquor from the shell. Discard the shells.
Place the flour in a bowl. Place the eggs in another bowl and whisk with 2 tablespoons water. Place the bread crumbs in a third bowl. Season the flour and bread crumbs with salt and pepper. Dredge the oysters in the flour first and tap off the excess. Next dip them in the egg mixture and then in the bread crumbs.
In a small saucepan heat 1-inch of oil to 375°F.
For the dressing, in a bowl, whisk together the reserved oyster liquor, the garlic, mustard, lemon juice, mashed anchovies and egg yolk until well blended. Add the olive oil slowly in a steady stream and whisk until smooth. Season to taste with salt and pepper.
Deep fry the oysters, a few at a time, until golden, 1 minute. Remove with a slotted spoon and drain on paper towels.
Place the lettuce in a large bowl and toss with the dressing until the leaves are coated. Add half of the Parmigiano and toss again. Place on serving plates and top each plate with 3 oysters and sprinkle the top with the remaining Parmigiano. Serve immediately.