Line your work surface with paper towels. Arrange the slices of eggplant on top of the paper towels. Sprinkle salt over the eggplant and let it sit for 20 minutes.
Place the potatoes into a pot filled with cold water. Bring the water to a boil and cook the potatoes for 15 minutes or until tender. Drain the potatoes and set them aside to cool. When the potatoes are cool enough to touch, slice them into ¼-½ inch thick slices.
Heat the olive oil in a large pan over medium high heat. Add in the lamb. Cook and crumble the lamb until it has browned and fully cooked. Then add in the onion and garlic. Sauté until the onions turn translucent and then mix in the tomato paste and whole tomatoes. Use a wooden spoon to crush and break apart the whole tomatoes. Stir in the cumin seeds, rosemary, cinnamon, and salt to taste. Reduce the heat to low so that the mixture is simmering. Simmer for about 50 minutes.
In the meantime, preheat the oven to 400˚F. Pat the salted eggplant dry with paper towels. Heat a few tablespoons of vegetable oil to a pan, enough to coat the bottom of it, over medium-high heat. Fry the eggplant slices on both sides until golden brown then transfer them to a plate lined with paper towels to drain.
Melt the butter in a sauce-pot over medium heat. Whisk in the flour and mix until it turns into a paste. Gradually pour in the milk while whisking constantly. Reduce the heat so that the sauce is simmering. Simmer for 3-4 minutes, while whisking constantly, until the sauce thickens. Remove the sauce-pot from the heat and mix in the egg, nutmeg, and salt and pepper to taste.
Spray a large cast iron with cooking spray. Arrange the sliced potatoes in an even layer on the bottom of the dish. Sprinkle lightly with salt. Then layer the eggplant slices on top. Spread the meat sauce evenly over the eggplant then sprinkle the parmesan on top. Finish with pouring the cream sauce over top. Bake it in the oven for 45 minutes until the top is set and golden brown. Enjoy!
