Trim and halve the Eggplant lengthwise (or make deep slits if you prefer whole), then sprinkle the cut surfaces with Salt and let them sit for 20–30 minutes to draw out bitterness; rinse and pat dry.
Heat a generous amount of Extra-Virgin Olive Oil in a large skillet over medium heat and fry the prepared eggplants until golden and softened on both sides; transfer to a plate and set aside.
In the same pan add a little more Extra-Virgin Olive Oil if needed and sauté thinly sliced Onion until translucent, then add minced Garlic and sliced Turkish Green Pepper and cook until softened.
Stir in chopped Tomato, a pinch of Sugar, Salt to taste and Ground Black Pepper; simmer the mixture until it becomes a thick, saucy filling, then finish with a splash of Lemon Juice to brighten the flavors.
Create a cavity in each eggplant half (or spoon open the slits) and fill generously with the tomato-onion mixture; arrange the stuffed eggplants in a shallow baking dish.
Pour a little Water into the bottom of the dish and drizzle more Extra-Virgin Olive Oil over the stuffed eggplants, cover the dish and simmer on the stovetop over low heat or bake in a moderate oven until the eggplants are very tender and the flavors meld.
Let the dish cool to room temperature so the sauce settles, then sprinkle chopped Parsley over the top and add an extra drizzle of Extra-Virgin Olive Oil and a little more Lemon Juice if desired.
Serve Imam Bayıldı at room temperature with crusty bread or rice to soak up the olive oil–tomato sauce.
