Begin by laying out the eggplant slices on paper towels, seasoning them lightly with salt. Leave them for about 30 minutes to draw out excess moisture, then dab them dry.

Heat olive oil in a skillet over a high flame. Fry the eggplant slices until each side turns a golden brown, roughly 2 to 3 minutes per side. Remove and drain on paper towels.

Using the same skillet, melt a tablespoon of butter over medium heat. Add the ground beef, onions, and garlic. Season with salt and black pepper. Cook, stirring occasionally, until the beef is thoroughly browned, about 8 to 10 minutes.

Stir in the parsley, fines herbes, cinnamon, and 1/4 teaspoon nutmeg. Add the tomato sauce and red wine, blending well. Let the mixture simmer for 20 minutes, then cool slightly before folding in the beaten egg.

In a separate saucepan, gently heat the milk just until it starts to bubble around the edges but is not boiling.

Concurrently, melt 1/2 cup butter in another skillet over medium heat. Whisk in the flour until the mixture becomes smooth. Reduce the heat and slowly add the heated milk, continuously whisking until the sauce thickens. Season the béchamel sauce with salt and ground white pepper.

Preheat your oven to 350 degrees F (175 degrees C). Lightly grease a 9x13-inch baking dish.

Place a single layer of eggplant slices at the bottom of the prepared dish.

Top the eggplant with the meat mixture, then sprinkle over 1/2 cup of Parmesan cheese. Layer the remaining eggplant slices on top, followed by another 1/2 cup of cheese.

Evenly pour the béchamel sauce over the top layer, then sprinkle with the remaining 1/4 teaspoon nutmeg. Finish with the remaining cheese.

Bake in the preheated oven for about 1 hour, or until the top is bubbly and golden brown.

Serve the moussaka hot from the oven and enjoy!