Preheat your oven to 400 degrees Fahrenheit. Prepare two large baking sheets by lining them with parchment paper.

Slice your eggplants and potatoes into rounds. Brush both sides of the vegetable slices with olive oil and sprinkle them with salt and pepper. Arrange them in a single layer on the baking sheets. Roast the vegetables for about 20 to 25 minutes until they become tender and slightly golden.

While the vegetables roast, heat a large skillet over medium heat and add a splash of olive oil. Add the diced onions and sauté until translucent. Stir in the minced garlic and cook for another minute.

Add the ground meat to the skillet and break it apart as it browns. Once the meat is no longer pink, drain any excess fat. Stir in the tomato paste, crushed tomatoes, oregano, cinnamon, and nutmeg. Let the sauce simmer on low heat for about 15 minutes.

In a medium saucepan, melt the butter over medium heat. Whisk in the flour to create a smooth roux. Gradually pour in the milk while whisking constantly until the sauce thickens. Remove from heat and whisk in the egg yolks and half of the cheese.

Assemble the Easy Moussaka in a 9x13 inch baking dish, starting with a layer of roasted potatoes, followed by eggplant, meat sauce, and another layer of eggplant if desired. Pour the Béchamel sauce over the top and sprinkle with remaining cheese.

Lower the oven temperature to 350 degrees Fahrenheit and bake for 45 to 50 minutes until bubbly and golden brown. Let it rest for at least 20 minutes before slicing.