01 - Preheat oven to 400°F. Brush eggplant and potato slices on both sides with 2 tablespoons olive oil. Arrange in a single layer on parchment-lined baking sheets and bake for 20 minutes, flipping halfway, until golden and tender. Set aside.
02 - Heat 2 tablespoons olive oil in a large skillet over medium heat. Sauté onion for 4–5 minutes until soft, then add garlic and cook for 1 minute. Stir in tomato paste, diced tomatoes, lentils, oregano, cinnamon, parsley, salt, and pepper. Simmer for 10 minutes until thickened. Remove from heat.
03 - Melt butter in a saucepan over medium heat. Whisk in flour and cook for 1 minute. Gradually add milk, whisking constantly to prevent lumps. Cook until thickened, about 5 minutes. Remove from heat, then stir in nutmeg, cheese, and a pinch of salt. Let cool slightly and whisk in the egg.
04 - Reduce oven temperature to 375°F. In a 9x13-inch baking dish, layer half the potato slices, then half the eggplant, followed by half the lentil mixture. Repeat layers. Pour béchamel sauce evenly over the top.
05 - Bake for 35 to 40 minutes until golden and bubbling. Allow to rest for 15 minutes before slicing and serving.