Heat 1 tablespoon of olive oil in a large pan over medium heat. Add the finely chopped yellow onion and sauté until soft and golden. Stir in the minced garlic and cook for about 1 minute until fragrant. Add the ground beef and cook, breaking it up with a spoon, until fully browned. Stir in the tomato paste and fry for a couple of minutes. Deglaze the pan with the red wine, scraping up any browned bits. Pour in the tomato purée (passata) and beef stock, then mix in the fresh parsley, chopped thyme, bay leaf, salt, granulated sugar, ground cinnamon, and black pepper. Bring to a simmer, then reduce the heat and let it gently simmer for 30 minutes, stirring occasionally, until thickened.
Arrange a few sheets of paper towel or a clean tea towel on a flat surface. Lay out the eggplant slices in a single layer and sprinkle both sides with a pinch of salt. Layer two sheets of paper towel over the eggplant, then add the zucchini slices. Add more paper towel, followed by the potato slices and another layer of paper towel on top. Press down gently to soak up excess moisture from all the vegetables. Let rest for at least 15 minutes. Removing moisture is essential here—it helps the veggies fry up crispier and prevents sogginess during baking.
In a large, deep pan, heat enough vegetable or olive oil (about 2 cups or enough to submerge the veggies) to 150°C/300°F. Carefully add the potato slices and fry on both sides until lightly golden and fork-tender. Remove and drain on fresh paper towels. Raise the oil temperature to 170°C/340°F and fry the zucchini slices until softened and lightly browned. Finish by frying the eggplant slices in the same way. After all the vegetables are cooked, let them drain on paper towels to remove as much excess oil as possible. I often work with two pans to speed things up, and sometimes I bake one vegetable to save time and reduce oil.
Melt the unsalted butter in a medium saucepan over medium heat. Stir in the all-purpose flour and cook, stirring constantly, for about 2 minutes to make a roux. Gradually whisk in the room temperature milk, ensuring no lumps form. Continue to whisk until the sauce has thickened and can coat the back of a spoon. Season with the salt, grated or ground nutmeg, and white pepper. Remove from the heat and stir in the freshly shredded pecorino romano cheese until smooth. Quickly whisk in the egg yolks until fully incorporated. Take 1/2 cup of this béchamel sauce and stir it into the beef mixture from Step 1. For an extra-silky sauce, I like to use room temperature milk and whisk vigorously to prevent lumps.
Preheat your oven to 180°C/350°F. In a large baking dish, arrange a layer of fried potato slices to cover the bottom, overlapping if needed. Sprinkle generously with chopped parsley, grated pecorino romano, and a pinch of salt and pepper. Next, add a layer of fried zucchini slices and repeat with parsley, pecorino, salt, and pepper. Add half of the fried eggplant slices, again seasoning with salt and pepper. Spread the beef mixture (now combined with some béchamel) evenly over the vegetables. Add the remaining eggplant slices on top of the beef layer, then pour all the béchamel sauce over to cover the top smoothly.
Finish the moussaka with a final sprinkle of pecorino romano cheese. Place the assembled dish in the oven and bake at 180°C/350°F for 35–45 minutes, or until the top is golden and lightly charred. Let the moussaka rest for at least 15 minutes before slicing and serving—this step is crucial to help it hold its shape. I find that the flavors also meld together even better if you let it sit a while.