How to Make It
Preheat the oven to 375°. In a skillet, heat the olive oil. Add the onion and garlic and cook over moderate heat until soft. Transfer to a bowl; let cool. Stir in the cheeses, parsley and basil; season with pepper.
In a shallow bowl, beat the egg. Whisk in the milk. Spread the flour and bread crumbs in separate shallow bowls. Season the bread crumbs with salt and pepper. Select 8 pairs of uniform eggplant slices; reserve the rest for another use. Dip the eggplant slices in the flour, then in the egg and finally in the bread crumbs, pressing to help them adhere. Transfer the coated eggplant to a wax paperlined baking sheet.
In a large skillet, heat the vegetable oil. Line a baking sheet with paper towels. Add the eggplant to the skillet in batches and fry over moderately high heat, turning once, until crisp and deeply browned, about 5 minutes. Drain on the paper towels.
Top 8 eggplant slices with the cheese mixture and cover with the remaining slices. Transfer the sandwiches to a baking sheet and bake for 10 minutes, until the cheese is melted. Drizzle the sandwiches lightly with pomegranate molasses and serve.