Mix 1/2 c salt with 8 c water in large pot. Slice top and bottom off eggplants. Cut thick strips of skin off the eggplants and give then a striped appearance. Slice eggplant into 1/4 rounds a d drop them into brine. Let the eggplant sit in brine 15 to 20 mins and let them dry.
Heat oil in skillet and brown ground meat. Halfway through add onions and red pepper. Add salt, garlic, cinnamon, cayenne pepper, ginger, pepper, oregano, and tomatoe paste. Mix well and cook 2 to 3 mins. Add red wine and bring to a simmer. Reduce heat and continue to simmer. Turn off heat and add lemon Zest send juice. Mix well.
Peel and slice potatoes into 1/4 rounds and boil in salted water for 5 to 8 mins. Want them undercooked but not crunchy.
Preheat oven to broil. Line a roasting pan with aluminum foil. Grease the inside with olive oil and place the eggplant on three foil and brush with oil. Broil 3 to 4 mins until lightly browned flip and brown other side.
Add milk to a pot and set over medium heat until steamy. Do not let milk simmer.
Heat butter in small pot and slowly whisk flour let roux simmer. Slowly pour milk into roux and stir constantly. Once all milk is added return to heat and add Bay leaf, nutmeg, and salt. Cook and stir about 15 mins and discard leaf.
Put egg yolks in bowl and whisk. Slowly pour a ladles worth of Bechamel onto eggs, constantly whisking. Slowly pour the egg mixture back into the Bechamel while whisking the mixture. Keep the sauce on very low heat to prevent boiling.
Heat oven to 350 and layer bottom of casserole with potaote, eggplant, meat sauce, repeat. Top half of cheese on top and label Bechamel over everything. Top with cheese and bake 45 mins.