Preheat the oven 180˚C fan / 200˚C / 356˚F convection / 392˚F.
Bring a large pan of water to the boil. Add the pasta and cook for 1 minute less than the instructions on the packet say to cook it for.
To make the minced beef sauce
While the pasta cooks, heat the oil in a medium sized saucepan and add the chopped onion. Cook over a medium heat for 7-10 minutes, until softened.
Add the minced beef and cook until browned, breaking up with a spoon. This will take about 10 minutes. Drain any fat.
Add the crushed garlic and tomato puree / paste and cook for 1 minute before adding the ground cinnamon, ground cloves, bay leaf and tomato puree.
Cook for 1 minute then tip in the chopped tomatoes, stock and a pinch of salt and black pepper. Bring to the boil then turn the heat down and simmer gently for 15-20 minutes until the sauce has thickened slightly.
To make the bechamel
While the meat sauce cooks, gently melt the butter in a medium saucepan over a medium heat.
As soon as the butter has melted, sprinkle in the flour. Stir well to combine and cook for 1-2 minutes.
Add the milk a little at a time, stirring vigorously or whisking with a ballon whisk after each time.
When you’ve added half the milk, use a balloon whisk to stir in the rest of the milk.
Turn the heat down, add a pinch of nutmeg, season with black pepper and cook for 5 minutes, stirring every so often.
Once the sauce is thick and the flour has cooked, take the pan off the heat and leave to cool for 5 minutes.
To assemble the pastitsio
When the pasta is cooked, drain and then stir in the egg white.
Tip the pasta in to a 26 x 20 cm (10 x 8 inch) deep ovenproof dish.
Spoon the beef sauce over the pasta and spread out in an even layer.
Add the egg yolk to the cooled bechamel sauce and whisk in quickly to combine.
Pour the bechamel over the beef mince and spread out with a spoon, making sure the sauce is covering all the meat sauce.
Sprinkle over the cheeses and place in the preheated oven to bake for 30-40 minutes until bubbling and golden brown and bubbling.
Leave to cool for 10-15 minutes before serving.
Notes
MAKE AHEAD / STORAGEMake ahead - you can prepare the individual elements ahead of time, and then assemble just before baking, or assemble and store in the fridge covered, for up to 2 days.Leftovers - store leftovers in the fridge in an airtight container for up to 3 days. Reheat in the microwave until piping hot.Freeze - freeze leftover, thaw / defrost in the fridge before reheating until piping hot.