slice the eggplant lenghtwise in 1/3 inch thick slices.
Salt generously, and lay out on a parchment lined baking sheet for about 30 minutes.
Meanwhile, brown meat until meat is all cooked and has rendered it's fat.
Add salt and pepper.
Using a slotted spoon, spoon the meat out of a pan and into a bowl to reserve. Add the olive oil, and sweat the onions and garlice.
Stir in remaining ingredients, and add the meat back in.
Cover with the 1/2 cup of hot water, more or less if needed until just covered and simmer on low until thick and fragrant, about 45 minutes.
Let cool slightly, then stir in: 1/2 cup chopped parsley and large egg, well beaten.
Set aside while you cook the eggplant.
Preheat the broiler.
Brush 2 baking sheets with olive oil.
Rinse the eggplant slices and pat dry.
Place on the baking sheets and brush with olive oil. Broil for approx 3-5 minutes, until softened and slightly brown.
You can also bake in a 350° oven until soft and slightly browned.
Leave oven to 350°.
Grease a 3 qt baking dish, and place an even layer of eggplant, and spread meat mixture over the eggplant.
Bake for 30 minutes.
Meanwhile, beat together: large eggs, 1/4 cups plain Greek yogurt, drained, pinch of paprika, salt and pepper.
Cover the casserole with mixture, and top with 1/2 cup grated Parmesan cheese and return to the oven to bake for 30 more minutes, until golden.