Wash and peel eggplants; slice 3/4 inch thick, discarding stem and bottom end pieces. Sprinkle slices with salt; place in bowl, cover and set aside 1/2 hour.
Pour off any liquid which has gathered around eggplant slices; wipe each slice with paper toweling, dip in flour, coating each side well.
Heat 1/4 cup oil in 10-inch skillet over moderate heat. saute slices of eggplant until golden brown. Place eggplant slices on heated platter in 200° oven while preparing the rest of the dish.
Beat eggs with whisk until well mixed. Add chopped scallion, soy sauce and sugar; mix well.
Place remainder of oil in skillet; add egg mixture. Cook over very low heat until eggs begin to set. Using fork, break up into small pieces after egg mixture has become fairly firm.
Place eggs over sauteed eggplant and serve at once.