Step 1

Prepare the Eggplant: Place the eggplant in a colander, sprinkle evenly with the salt, and toss with your hands. Let it sit for 30 minutes to 1 hour, then blot dry with paper towels or a clean dish towel. Line a baking sheet with heavy-duty aluminum foil. Directly on the foil, toss the salted eggplant with the oil, then spread it into a single layer.

Step 2

Prepare the Potatoes: On a separate baking sheet (do not line with foil), toss the potato slices with the oil and salt, arranging them in a single layer.

Step 3

Position two oven racks in the middle and lower third of the oven, then preheat to 450°F.

Step 4

Place the eggplant on the middle rack and the potatoes on the lower-middle rack. Roast until the eggplant is softened and lightly browned and the potatoes are tender, 30 to 35 minutes. Toss the potatoes once halfway through to prevent sticking. Set the vegetables aside and reduce the oven temperature to 400°F.

Step 5

Make the Meat Sauce: In a Dutch oven or large pot, heat the oil over medium heat until shimmering. Add the onion and cook, stirring occasionally, until softened, about 5 minutes. Add the garlic and stir constantly until fragrant, about 1 minute. Do not brown. Add the wine, paprika, oregano, red pepper flakes, and cinnamon; increase the heat to medium-high, scraping up any browned bits from the bottom of the pot, and cook until the wine has almost completely evaporated, 2 to 3 minutes. Add the beef, breaking it up with a wooden spoon, and cook until no pink remains, 4 to 5 minutes. Stir in the tomatoes, salt, and sugar, then lower the heat to medium. Cook uncovered, stirring occasionally, until thickened, 6 to 8 minutes. Set aside.

Step 6

Prepare the Béchamel: In a medium saucepan, melt the butter over medium heat. Whisk in the flour and cook, until lightly golden, about 1 minute. Gradually add the milk, about 1 cup at a time, whisking constantly. Increase heat to medium-high and cook, whisking frequently, until thick, smooth, and sputtering, 3 to 5 minutes. It should be the consistency of very runny mashed potatoes. Off the heat, whisk in the cheese, salt, and nutmeg. Whisk in the egg yolks one at a time. Set aside.

Step 7

Assemble the Moussaka: Lightly grease a 9x13-inch baking dish with nonstick cooking spray or olive oil. Arrange the roasted potatoes in an even layer, followed by the eggplant, pressing to create a compact layer. Spread the meat sauce evenly over the eggplant, then spread the béchamel evenly over top.

Step 8

Place the baking dish on a rimmed baking sheet lined with foil to catch any spills. Bake until the top is lightly browned in spots and bubbling at the edges, 30 to 35 minutes. To ensure the dish sets up properly, let it sit at room temperature for 30 minutes before slicing.