Preheat the oven to 400 degrees F.
Heat 2 tablespoons EVOO in a medium Dutch oven over medium-high heat. Add the ground lamb and cook until well browned. Season with salt and pepper, then stir in the garlic, chile pepper, onions and oregano and cook for 5 minutes. Stir in the tomato paste and cook for 1 minute. Deglaze with the wine, stirring and scraping up any browned bits from the bottom of the pot with a wooden spoon. Add the stock, lemon zest, bay leaf, cinnamon stick and tomatoes and simmer until thickened, about 30 minutes, stirring occasionally.
Meanwhile, cut a thin slice from two opposite sides of each eggplant, removing some of the skin. Turn the eggplant cut-side up, then cut lengthwise into 1/4-inch-thick planks. Sprinkle with salt and drain in a colander for 20 minutes. Pat dry.
Beat the egg whites with a splash of water in a shallow dish. Mix the panko with the remaining 4 tablespoons EVOO in another dish until well coated. Add half the cheese, the parsley, granulated garlic and granulated onion to the panko and mix well.
Set a wire rack over each of 2 baking sheets. Dip each eggplant slice in the egg whites, then coat with the panko mixture, pressing to help it adhere. Arrange on the wire racks. Bake until crisp and golden, 25 to 30 minutes.
Melt the butter in a saucepan over medium heat. Add the flour and cook, whisking, for 1 minute. Whisk in the milk and season with salt, pepper and a few grates of nutmeg. Simmer at a low bubble until thick enough to coat the back of a spoon. Lightly beat the egg yolks in a medium bowl. Slowly pour in some of the sauce, whisking constantly to temper the yolks. Pour the mixture back into the saucepan and remove from the heat.
Make two layers of eggplant and lamb mixture in a medium casserole dish. Pour the sauce over the top and sprinkle with the remaining cheese. Bake until browned and bubbling, 30 to 40 minutes.
Cook's Note: The casserole can be covered and refrigerated for a make-ahead meal. Reheat, covered, until heated through, then sprinkle with more cheese and bake, uncovered, to crisp the top.