1. Prepare the vegetables: slice the eggplants into 1cm thick. Season with salt and set aside for 30 minutes. Meanwhile peel the potatoes and slice them.
2. Wash the eggplants well and pat them dry. Fry the eggplants and potatoes until golden. Transfer to a paper towel to get rid of access oil. For a lighter version place the eggplants and potatoes in a baking pan, drizzle with olive oil and bake and golden.
3. Prepare the meat mixture: heat olive oil in a large pan over medium heat. Add chopped onions and sauté for 3-4 minutes. Add crushed garlic and sauté for 2-3 minutes more.
4. Add the meat and cook, stirring, until the beef is no longer pink. And salt, pepper, cinnamon and thyme, stir well. Add tomato paste and stir. Add bay leaf, tomato sauce and stir well. Add beef broth, stir and bring to a boil. Reduce the heat to low and simmer until thickens. Remove from heat and set aside.
5. Prepare the béchamel sauce: heat 1 litter of milk. In a medium saucepan over low heat melt butter, when the butter is melted, add flour and whisk continuously, until smooth paste forms. Gradually add the warm milk while continually whisking to prevent lumps. Whisk until the sauce is smooth and thick. Remove from heat and add pinch salt, black pepper, nutmeg, parmesan and egg yolks, whisk until smooth.
6. Preheat oven to 180C (360F).
7. Assemble the moussaka: add 4-5 tablespoons of the béchamel sauce to the meat mixture and mix. Layer the potatoes in a 13"X8.5" (33X22cm) ovenproof dish, then layer half of the eggplants. Pour the meat mixture and spread evenly. Layer the remaining eggplants and pour the béchamel sauce. Grate some parmesan on top.
8. Bake for 40-50 minutes or until golden brown. Remove from oven and let cool for at least 45 minutes before cutting.