PREPARE EGGPLANT: Cut off the stem sections of 2 large fresh eggplants. Peel eggplant using a sharp vegetable peeler. Cut eggplants lengthwise in even 1/8" thick slices. Pour 1/4-1/3 cup extra virgin olive oil into a large microwave-safe bowl. Mash 2 garlic cloves using a garlic press and add to oil. Add 1/4 teaspoon fine sea salt and 1/4 teaspoon fresh ground black pepper. Stir. Heat mixture in microwave about 30-45 seconds on high. Rub or brush the sliced eggplant with the oil mixture until lightly coated. Wipe the bowl clean with a paper towel and set aside. Arrange seasoned eggplant single-layer onto a flat-ridged or press-type grill on medium-high heat. When the eggplant has dark grill marks, turn and grill other side the same (skip turning eggplant if using a press-type grill). Allow eggplant to "sweat" until needed. Sprinkle, then pat, finished eggplant slices liberally using 1/2 cup powdered parmesan cheese.
IN a large food processor, chop 1 large onion, 1 medium bell pepper, one handful pitted kalamata olives, 1 handful flat leaf parsley leaves, and 8-12 garlic cloves.
HEAT 2 tablespoons extra virgin olive oil in a large saucepan over medium heat; ADD the above chopped vegetables, 1 1/2 lbs lean ground beef, 1 teaspoon fine sea salt and 1/2 teaspoon fresh ground black pepper; SAUTE until meat is browned and vegetables have softened.
ADD 1 (14 ounce) can diced tomatoes, 3/4 cup dry greek red wine, 1 (6 ounce) can tomato paste, 2 tablespoons red wine vinegar, 2 teaspoons greek honey, 1 1/4 teaspoons crushed dried oregano, 1 teaspoon ground cinnamon, 1/4 teaspoon ground allspice, 1/4 teaspoon freshly grated nutmeg, 1/2 tablespoon ouzo or 1/4 teaspoon pure anise extract, 1/4 teaspoon fresh grated lemon zest, 1/4 teaspoon crushed dried mint, 1/4 teaspoon fresh ground white pepper, 1 pinch crushed red pepper flakes, and 3 tablespoons grated parmesan cheese; STIR well; COVER; REDUCE heat; SIMMER for 45 minutes or longer (sauce will be thick); RE-SEASON sauce to taste with fine sea salt if needed (leave sauce just slightly under-salted since sauce will concentrate while baking).
INTO the previously wiped large bowl, separate 4 large eggs, retaining the yolks in bowl (refrigerate egg whites sealed, for another use while fresh);.
WHISK in 4 cups whole milk until smooth; ADD 2 teaspoons extra virgin olive oil, 2 teaspoons fresh lemon juice, 1 level teaspoon fine sea salt, 1/2 teaspoon fresh ground white pepper, 1/4 teaspoon freshly grated nutmeg, 1/8 teaspoon garlic powder, and 1 pinch cayenne pepper; WHISK again until blended; SET aside.
MELT 1/2 cup salted butter over medium heat; ADD 1/2 cup all-purpose flour and cook for just one minute; POUR milk and egg mixture all at once into roux while whisking constantly; CONTINUE whisking often until sauce thickens up and begins to bubble; REMOVE from heat; WHISK in 3/4 cup powdered parmesan cheese until smooth and glossy; COVER loosely with plastic wrap; BLEND 1/2 cup of the BECHAMEL into the fully-simmered SAUCE.
PREHEAT oven to 350 F; OIL a 2-3 quart casserole dish with olive oil; SPREAD 1/2 (one half) of the EGGPLANT single-layer in bottom of baking dish; POUR the entire SAUCE mixture over top then smooth; ADD the remaining EGGPLANT over the SAUCE; POUR all of the BECHAMEL sauce over the eggplant; SMOOTH bechamel sauce. NOTE: YOU CAN SPRINKLE THE TOP OF CASSEROLE NOW LIGHTLY WITH GRATED PARMESAN CHEESE (PLUS MINCED FRESH PARSLEY IF DESIRED) OR YOU CAN GARNISH WHILE STILL HOT, JUST AFTER BAKING.
BAKE for 1 hour; ALLOW to rest 20 minutes before slicing.
SERVE and enjoy!