Arrange the eggplant slices on the baking sheets, sprinkle both sides with 1 teaspoon salt, and let stand for 20 minutes. Pat very dry with clean towels.

Heat the oven to 425°F. Brush the eggplant and potato slices with 3 tablespoons olive oil. Roast in a single layer, flipping once, until tender and lightly browned, 25 to 35 minutes. Reduce the oven to 375°F.

Heat the remaining 1 tablespoon olive oil in a large skillet over medium heat. Cook the onion for 6 minutes until soft. Add the garlic and cook for 30 seconds.

Add the ground beef, breaking it into small pieces. Cook until no pink remains and the meat reaches 160°F, about 8 minutes. Spoon off excess fat if needed.

Stir in the tomato paste for 1 minute. Add the wine and simmer for 2 minutes. Add the tomatoes, oregano, cinnamon, allspice, pepper, and remaining 1/2 teaspoon salt. Simmer uncovered until thick rather than watery, 20 to 25 minutes. Taste and adjust seasoning.

Melt the butter in a medium saucepan over medium heat. Whisk in the flour and cook for 2 minutes. Gradually whisk in the warm milk. Cook, whisking, until very thick and bubbling, 7 to 10 minutes. Season with nutmeg and a pinch of salt.

Remove the béchamel from the heat. Whisk 1 cup of the hot sauce slowly into the beaten eggs, then whisk the egg mixture back into the saucepan. Stir in 3/4 cup cheese.

Lightly oil a 9 x 13-inch baking dish. Layer in the potatoes, half the eggplant, all the meat sauce, and the remaining eggplant. Spread the béchamel evenly over the top and sprinkle with the remaining 1/4 cup cheese.

Bake at 375°F until the top is deeply golden and the center is hot, 40 to 45 minutes.

Let the moussaka rest for at least 25 minutes. This is not optional theater—the layers set as they cool, giving you tidy slices instead of a delicious landslide.