Preheat oven to 350 degrees F (175 degrees C). Spread eggplant slices on 2 baking sheets. Brush each side lightly with 1 tablespoon olive oil.
Bake in the preheated oven until slices are soft and floppy, about 25 minutes.
Heat 1 tablespoon olive oil in a skillet over medium heat. Add onion; cook and stir until softened, 3 to 5 minutes. Stir in garlic, cinnamon, and oregano. Add chicken strips; cook until browned, about 5 minutes. Stir in red wine, water, and tomato paste. Simmer sauce until thickened, 20 to 30 minutes. Stir in parsley, salt, and pepper.
Measure cornstarch into a bowl. Mix in yogurt slowly until no lumps remain. Mix in eggs and nutmeg.
Grease a baking dish with remaining 1 tablespoon olive oil. Cover the bottom with a layer of eggplant slices. Top with 1/2 of the chicken mixture. Repeat layers once more, ending with eggplant slices on top. Pour yogurt mixture on top, carefully smoothing it out.
Bake in the preheated oven until topping is golden and bubbling, 40 to 45 minutes. Let moussaka rest for 30 minutes to ensure slices don't fall apart.