Preheat the oven to 400°F (200°C).
Arrange the eggplant slices on baking sheets and brush both sides with 2 tablespoons olive oil. Season with salt and pepper.
Roast the eggplant in the oven for 20 minutes, flipping halfway through, until tender and golden. Remove and set aside.
Reduce oven temperature to 350°F (175°C).
Heat 1 tablespoon olive oil in a large skillet over medium heat. Add the chopped onion and cook until softened, about 5 minutes.
Add the minced garlic and cook for 1 minute until fragrant.
Add the ground beef to the skillet and cook until browned, breaking it up with a spoon, about 7 minutes.
Stir in the diced tomatoes, tomato paste, dried oregano, ground cinnamon, salt, and pepper. Simmer for 15 minutes, stirring occasionally, until the sauce thickens slightly.
While the meat sauce simmers, prepare the béchamel sauce: melt the butter in a medium saucepan over medium heat.
Whisk in the flour and cook for 1-2 minutes until lightly golden, stirring constantly.
Gradually whisk in the milk, continuing to whisk until the sauce thickens and is smooth, about 5-7 minutes.
Remove the béchamel from heat and stir in the ground nutmeg, half of the grated Parmesan cheese, and the beaten eggs. Mix quickly to combine and prevent curdling.
In a 9×13 inch baking dish, layer half of the roasted eggplant slices evenly on the bottom.
Spread all of the meat sauce evenly over the eggplant layer.
Add the remaining eggplant slices on top of the meat sauce.
Pour the béchamel sauce evenly over the top layer of eggplant.
Sprinkle the remaining Parmesan cheese over the béchamel.
Bake uncovered in the preheated oven for 40 minutes, until the top is golden and bubbly.
Let the moussaka rest for 15 minutes before slicing and serving.