Preparation

• Trim off the ends of the eggplant, then slice into ¼-thick slabs. Spread the eggplant in one layer and sprinkle with salt. Let set for 30 minutes to 'sweat out' its bitterness.
• Heat 2 tablespoons olive oil in a large skillet over medium heat. Add the onion and stir regularly until slightly golden brown, about 5 minutes. Add the ground lamb or beef and toss regularly until fully browned. Pour off any excess fat, then return the skillet to medium heat.
• Stir in the dried oregano, cinnamon, pepper, nutmeg, and paprika. Add the wine and boil for 1 minute to reduce, then stir in the canned tomatoes, sugar, and hot beef broth. Simmer over medium-low heat until rich and fragrant, 20 to 30 minutes.
• Turn the broiler of your oven to high. Brush a large sheet pan with extra virgin olive oil. Pat the eggplant slices dry, removing excess salt, and assemble in one layer on the prepared pan. Brush or coat the eggplant generously with olive oil on both sides.
• Place the sheet pan about 6 inches away from the broiler. Broil the eggplant briefly, turning over so that both sides are softened and golden brown. Remove from the oven and set aside.
• Turn off the broiler and preheat your oven to 350°F. Lightly oil a 9 ½" x 13" oven-safe baking dish.
• In a large saucepan, heat the olive oil over medium-high heat until shimmering but not smoking. Stir in the flour, salt, and grind/pinch of black pepper. Cook, stirring continuously, until golden. Gradually add the warmed milk, whisking continuously. Continue to cook, stirring occasionally, over medium heat until thickened enough to coat the back of a wooden spoon, 5 to 7 minutes. Season with the nutmeg.
• Add the eggs to a small bowl. Whisk in a ladleful of the hot bechamel mixture to temper, then slowly whisk the egg mixture back into the bechamel. Continue to stir or whisk the mixture bringing to a gentle boil for just 2 more minutes. Taste and adjust the seasoning. Remove from the heat and allow to cool and thicken a little more.
• Layer half the eggplant slices on the bottom. Add the meat sauce and spread well, then top with the remaining eggplant slices. Pour the bechamel on top and spread to cover all the eggplant, then sprinkle with the breadcrumbs.
• Bake the moussaka casserole on the center rack of the heated oven for 45 minutes. If desired, transfer the baking pan to the top rack and broil briefly so that the top of the moussaka gains a nice golden brown color.
• Remove from the heat and let the casserole sit for 10 minutes. Slice into squares to serve.