To prepare the eggplants, place a grate over an open flame on a gas stove. Cook the eggplants for several minutes on all sides until the eggplants are yielded to gentle pressure with a fork. The goal is to cook them soft enough to mash. If you don’t have a gas stove, you can cook the eggplants on the grill in a similar fashion. See the footnotes above about cooking them in the oven.
Once they are soft enough set them aside on a plate and gently press on them with a fork to flatten them. Do not flatten them too much, you want them to hold together during the sautéing process later on.
To make the filling, heat a medium sized nonstick skillet over medium heat until hot. Add 2 tsp olive oil to the pan and swirl the pan to distribute the oil. Add minced garlic and diced onion to the pan and allow to cook stirring constantly until lightly browned. Add ¼ tsp kosher salt to the onions. Add chopped tomatoes and scallions, cook for 1 minute.
Then add the sardines to the pan. Break up the sardines into very small pieces. Add another ¼ tsp kosher salt and the lemon juice and stir well. Continue cooking this mixture until no more liquid remains in the pan, about 1-2 minutes over low heat depending on the juiciness of the tomatoes and sardines.
Beat the eggs in a medium bowl. Set a large nonstick pan over medium-high heat and heat until the pan is hot. Add 3 tbsp olive oil and wait until it is shimmering. Add the flattened eggplants (you may not be able to fit all the eggplants in the pan at once) cook on the first side for 30 seconds or so and then top the eggplant with a nice layer of filling to the edges.
Repeat with the other flattened eggplants in the pan. Drizzle an even amount of beaten egg onto each eggplant. Cook for several more minutes turning the heat down to low if necessary. Tilt the pan and use a spoon to ladle the hot oil over the tops of the eggplant to cook some of the beaten egg on top. Then use a spatula to flip the eggplant over and cook until heat through and browned. Repeat with any other eggplants left. Serve immediately with sliced scallions on top.