Place the eggplant slices in one layer on two paper towel-lined sheet pans. Sprinkle the eggplant slices with 1 teaspoon of salt, flip the eggplant over, and sprinkle an additional teaspoon of salt on the other side of the slices. Set the pan aside (ideally in direct sunlight) for at least 1 hour and up to 4 hours. Pat the eggplant dry with paper towels on both sides to remove the excess moisture and salt, and place the eggplant on fresh paper towel-lined sheet pans. 

Heat ½ inch of oil in a wide pan over medium heat until shimmering but not smoking. Place the flour in a wide bowl, add ½ teaspoon of black pepper and ½ teaspoon of salt, and mix well. Place the beaten egg in a second wide bowl.

Dredge a piece of eggplant in flour on both sides, dip it in the beaten egg, and then in the flour again to coat both sides. Gently place the eggplant in the hot oil and fry it for 6 minutes, flipping halfway, until golden on both sides. Transfer to paper towel-lined sheet pans. Repeat the dredging and frying with the remaining eggplant slices, working in batches to avoid overcrowding the pan. 

Prepare the sauce: Add all the sauce ingredients, except for the tomato paste and water, into a small pot over medium heat. Cook the sauce for about 5 minutes, stirring constantly, until fragrant and the garlic has softened. Add the tomato paste and water, and stir well. Bring the mixture to a simmer and remove from the heat. 

Preheat the oven to 350°F. Arrange the eggplant slices in a 9x13-inch baking dish and pour the sauce over them. The eggplant should be almost completely covered with sauce. Cover the dish with a lid, or seal with a layer of parchment paper and aluminum foil on top. Transfer the dish to the oven and bake for 50 minutes. Remove the cover from the dish, add the lemon juice (if using), and bake for 10 more minutes, until the top is nicely browned. Serve immediately.