Roast the vegetables: Preheat the oven to 210°C (410°F). Slice the eggplant and potatoes about 5 mm (3/16 inch) thick. Toss with half the olive oil and arrange in a single layer on baking sheets. Roast for approximately 25 minutes, turning halfway through, until tender and lightly golden.
Prepare the meat sauce: Meanwhile, heat the remaining olive oil in a large skillet over medium heat. Add the chopped onion and cook for about 8 minutes, until softened. Add the ground beef and cook, breaking it up with a spoon, until browned. Stir in the passata, cinnamon, black pepper, and half the salt. Simmer uncovered for approximately 25 minutes, stirring occasionally, until the sauce is thick and most of the excess liquid has evaporated.
Make the béchamel: Melt the butter in a saucepan over medium heat. Add the flour and cook, stirring continuously, for 2 minutes. Gradually whisk in the milk until smooth. Simmer gently for about 5 minutes, stirring regularly, until thickened. Remove from the heat and allow to cool for several minutes before whisking in the egg, grated cheese, and remaining salt.
Assemble the moussaka: Reduce the oven temperature to 180°C (350°F). Arrange the roasted potatoes in an even layer in a 24 cm (9½-inch) square baking dish. Add the roasted eggplant, followed by the meat sauce, spreading each layer evenly. Pour the béchamel over the top and smooth the surface.
Bake: Bake for 40–45 minutes, until the top is golden and the béchamel has set. Remove from the oven and let the moussaka rest for 25 minutes before slicing into four generous portions.