Leave the skin on the eggplants and use a fork to prick them over the whole surface.
If you have a gas stove, turn it on to medium heat, place the eggplants directly on the burner or on a rack, and char them for 4-5 minutes on all sides until they are tender and their skin is burnt. (Alternatively, bake them in a preheated oven at 180°C (350°F) set to fan for 30 minutes. Increase the temperature to 230°C (450°F) set to broiler, and bake them for another 10 minutes until their skin is burnt, making sure to turn them over continuously.)
Transfer the eggplants to a baking pan, immediately cover the pan with plastic wrap, and let the eggplants cool for 20-30 minutes.
Remove the plastic wrap and peel the eggplants with your hands, keeping the stem on.
Transfer the eggplants to a cutting board, and press them down with a spoon to spread them.
Season them with salt and pepper on both sides.
Put the flour into a baking pan, the eggs into a bowl -whisking them with a fork-, and the panko breadcrumbs into another bowl.
Place a frying pan over high heat, add the sunflower oil, and let it heat up well.
Spread some paper towels in a baking pan, and set it aside.
Dredge one eggplant at a time in the flour, then dip it into the eggs and the panko, and add it to the pan.
Cook each side for 1-2 minutes, use a slotted spoon to transfer the eggplant schnitzel to the baking pan, and press it with the paper towels to absorb the excess oil.
Follow the same process for the remaining 3 eggplants, and remove the pan from the heat.
Divide the schnitzels among plates, and crumble the feta cheese with your hands over the eggplants.
Serve with tomato sauce and basil leaves.
