Prepare a grill for indirect heat. If using a charcoal grill, build the hot coals on one side only. If using a gas grill, heat one side only to medium-high heat.
For the eggplant and meat sauce: Season the eggplant slices on both sides with salt and pepper and drizzle with olive oil. Turn to coat. Grill the eggplant slices straight over direct heat, flipping once, until tender and lightly golden brown on both sides, 5 to 7 minutes. You can move them from direct to indirect heat as needed. Transfer the eggplant slices to a baking sheet or a plate and set aside.
Place a 6-quart heavy bottomed saucepan over direct heat. Add a few tablespoons of olive oil along with the ground meat to the saucepot and season with salt and pepper. Cook, stirring to break up the meat, until well browned and caramelized, about 5 minutes. Then add the onions and garlic with a pinch of salt and cook until soft, about 5 minutes. Add the tomato paste and cook until rust colored, another minute. Add the wine and cook, stirring occasionally, until almost completely evaporated, about 5 minutes. Using butcher's twine, tie the bay leaves, cinnamon stick and oregano into a bundle. Add the crushed tomatoes and the spice bundle to the pot. Move the pot over indirect heat and simmer until thickened, about 30 minutes. Remove from the heat and discard the spice bundle.
For the bechamel sauce: In a heavy bottomed saucepot over direct heat, melt the butter. When butter has melted, whisk in the flour and cook until it forms a smooth paste, 3 to 4 minutes. Slowly whisk in half of the milk and once the mixture is smooth with no lumps, whisk in the remaining half and the nutmeg. Bring to a gentle boil and cook, stirring often, until thick and velvety, about 10 minutes. Remove from the heat and whisk in the pecorino. Set aside to cool slightly, then whisk in the egg yolks and lemon zest.
To assemble: Place the eggplant slices on the bottom of an enameled dish or cast-iron and cover with the meat sauce. Pour the bechamel all over the top, spreading it out into an even layer. Place over indirect heat, cover the grill and cook until light golden brown and bubbly on top, about 40 minutes.
Remove from the grill and let stand for 10 minutes before serving. Grate pecorino over the top and sprinkle with chopped parsley.
(Alternatively, you can bake the moussaka in a 400 degrees F oven for 45 minutes.)