Preheat the oven to 375F
Peel and slice the eggplant and zucchini lengthwise and lay them out on two pans. Sprinkle with olive oil and salt and pepper and put them in the oven for approximately 25 minutes.
In the meantime, heat 4 tbsp olive oil over medium-high heat in a large pot.
Add the chopped onion and stir until the onion is aromatic and translucent.
Add the minced garlic and stir for another minute.
Add the ground beef and cook thoroughly.
Crush the tomatoes with a pastry cutter (or your hand, as Yiayia does) and then add them to the ground beef mixture.
Add the sugar, salt, pepper, and parsley (either fresh or dry).
Cover and cook on low for 20 minutes.
Add parmesan cheese, then remove from heat add the two scrambled eggs (very slowly) and stir to combine.
Remove the eggplant and zucchini from the oven and prepare a 9x13 baking pan by lightly spraying the bottom with a non-stick oil.
Assemble the Moussaka by first laying a layer of eggplant on the base of the baking pan, then putting a layer (about half) of the ground beef mixture.
Add the zucchini, then another layer of ground beef. This should use up all your eggplant, zucchini, and ground beef mixture – but if you have any of the layers left over, feel free to add them to the pan now.
To make the Bechamel Sauce:
Add butter to a medium saucepan and once it’s melted, add the flour.
Stir for about one minute, then add the milk and nutmeg.
Stir until it thickens, then lower the heat.
Add the scrambled eggs by adding about 3 tbsp of the milk mixture into the eggs to bring them to temperature.
Pour them slowly into the milk mixture and then whisk them quickly to combine.
Pour the Bechamel sauce on top of the Moussaka and sprinkle Paprika lightly on top.
Bake for 45 minutes at 375.
Once it’s done, wait 10-15 minutes before you serve it to allow the layers to set.