Preheat your oven to 375°F (190°C). Prepare the vegetables and meat sauce in advance.
Eggplant: Salt the eggplant slices and let them sit for about 30 minutes to draw out bitterness. Rinse and pat dry before cooking. Arrange the eggplant slices on baking sheets, brush both sides with olive oil, and season with salt. Bake for 20-25 minutes until soft and lightly browned.
Potatoes: Boil the potato slices until just tender, about 5-7 minutes. Drain and set aside.
Meat Sauce: In a large pan, heat olive oil over medium heat. Sauté onion and garlic until translucent. Add the ground meat, breaking it up with a spoon, and cook until browned. Stir in the crushed tomatoes, cinnamon, allspice, salt, and pepper. Simmer for about 20 minutes until thickened. Set aside.
Béchamel Sauce: Melt butter in a saucepan over medium heat. Stir in flour to form a roux, cooking for 1-2 minutes without browning. Gradually whisk in warm milk until the sauce is smooth and thickened. Remove from heat, and slowly whisk in egg yolks and Parmesan. Season with nutmeg, salt, and pepper.
Assemble the Moussaka: In a large baking dish, layer potatoes, eggplant, and meat sauce. Repeat the layers until all ingredients are used, finishing with a layer of eggplant. Pour the béchamel sauce over the top, spreading evenly.
Bake for about 45 minutes, or until the béchamel is golden and the moussaka is bubbling. Let it rest for 10 minutes before serving.