Heat olive oil in a large pan over medium heat. Sauté the onion and garlic until fragrant and softened. Add the minced beef and cook until browned, breaking it up with a wooden spoon. Stir in tomato purée, chopped tomatoes, red wine, and seasonings. Simmer for 25 minutes until thick and rich. Set aside to cool slightly before layering.
Bring a large pot of salted water to the boil and cook the pasta until just al dente. Drain, then stir in butter while still warm to prevent sticking. Let it cool slightly before mixing in the beaten egg and grated cheese.
In a saucepan, melt the butter over medium heat. Add the flour and stir for one minute to create a smooth paste. Gradually whisk in the warm milk, stirring continuously until the sauce thickens. Season with nutmeg, salt, and pepper. Remove from heat and stir in the cheese and egg yolk for a creamy finish.
Preheat the oven to 180°C (160°C fan). Grease a medium-sized baking dish with butter or olive oil. Spread half of the pasta evenly on the bottom to form the base layer.
Spoon the meat sauce evenly over the pasta, pressing gently to compact it slightly. Smooth the surface before adding the next layer.
Place the remaining pasta on top of the meat mixture, spreading it evenly. This helps the layers stay distinct when sliced after baking.
Evenly pour the warm béchamel sauce over the pasta, using a spatula to smooth it across the surface. The sauce should fully cover the pasta for that signature creamy top.
Place the dish in the oven and bake for 40–45 minutes until the top is golden and slightly blistered. The aroma of cinnamon and nutmeg should fill the kitchen.
Allow the pastitsio to rest for 20 minutes before slicing. This helps it set and hold its layers beautifully when cut.
Slice neatly into portions and serve with a crisp Greek salad or roasted vegetables. Sprinkle a touch of grated cheese on top for a finishing touch.