Heat your oven to 450°. Line a baking sheet with parchment paper.
Place the eggplant slices in a large bowl and season with ½ tsp of salt and a good grind of black pepper. Pour in the oil, mix well to coat the slices, then spread them out on the prepared baking sheet.
Bake for 25 to 30 minutes, or until golden brown and cooked through. Remove from the oven and set aside. Decrease the oven temperature to 425°.
While the eggplants are roasting, make the tomato sauce. Place the oil in a medium saucepan and heat over med-high heat. Add the onion and cook for about 6 minutes, stirring occasionally, until it has softened and lightly browned. Add garlic and tomato paste and cook for another 30 seconds. Stir in the canned tomatoes, sugar, mint, Aleppo pepper (or chile flakes), water, ½ tsp salt, and a good grind of black pepper.
Bring to a boil, lower heat to medium-low, and cook for 20 minutes, stirring occasionally, until the sauce is thick and rich. Remove from the heat and set aside until ready to use.
To make the kofta, combine the beef, parsley, onion, garlic, grated tomatoes, tomato paste, cinnamon, allspice, nutmeg, Aleppo pepper, and olive oil into a large bowl with 1 ¾ tsp of salt and a good grind of black pepper. Mix well, then divide the mixture into 12 large balls. Shape into patties about 3 in wide and set aside.
Arrange the slices of eggplant in a single layer on the bottom of a flameproof roasting pan (or a 9x13 Pyrex pan). Place 1 kofta patty on top of each slice and top each with a slice of tomato, creating a kind of sandwich. Spoon a generous 1 tsbsp of the thick tomato sauce on top of each sandwich, spreading it out slightly so that it drizzles down the sides.
Cover the dish tightly with aluminum foil and bake for 20 minutes. Then increase the oven temperature to 475°, remove the foil and bake for a final 18 minutes.
Remove the roasting pan from the oven and, using a spatula, lift the kofta out of the liquid (don’t discard the liquid, though), trying to keep the eggplant slices intact. Place on a large platter or individual serving plates.
Top with basil leaves and enjoy.