Position an oven rack about 4 inches (10 cm) below the broiler and line a rimmed baking sheet with foil. Prick each eggplant a few times with a fork and place on the sheet.

Broil the eggplants, turning them every few minutes with tongs, until the skins are deeply blistered and the flesh is very soft, about 10 to 15 minutes. Transfer to a plate and let stand until cool enough to handle.

Peel away and discard the charred skins, leaving the stems attached if possible. Place each peeled eggplant on a cutting board or plate and gently flatten it lengthwise with a fork. Do not mash it completely; keep the flesh in one piece.

In a shallow bowl, beat the eggs with 1/4 teaspoon salt (1.5 g) and the black pepper. Sprinkle the flattened eggplants with the remaining 1/4 teaspoon salt (1.5 g).

Heat 1 tablespoon oil (15 mL) in a large nonstick skillet over medium heat. Dip 2 eggplants into the beaten egg, coating both sides and letting excess egg fall back into the bowl. Lay them in the skillet, then spoon a little of the remaining egg over any bare spots.

Cook until the underside is golden and the egg is set, about 2 to 3 minutes. Carefully flip with a wide spatula and cook the second side until golden and fully set, about 2 minutes more. Transfer to a plate.

Add the remaining 1 tablespoon oil (15 mL) and repeat with the remaining eggplants and egg mixture. Serve hot with steamed rice, ketchup, banana ketchup, or a vinegar dipping sauce, if desired.