Cook the pasta as per instructions until al dente. Set aside.
In a large pan or wok, fry the chopped onion in the oil on a medium heat until softened. Add the minced garlic and fry gently for a further 2 minutes.
Add the vegetarian mince and brown. It may be necessary to add additional oil to keep the mince moist. Add half of the thyme, the parsley, the cinnamon and half of the salt. Mix well for 1 minute.
You can make the tomato sauce by mixing 500ml of tomato puree and 500ml water or use canned. Add this to the mince and simmer for 5 minutes. Add additional water or reduce as necessary depending on how absorbent the mince is. Set aside. When cooled add one third of the beaten egg and mix well.
Make the béchamel sauce: Melt the butter in a large pan on a medium heat and slowly add the flour, whisking continuously. Slowly whisk in the milk and then add the rest of the salt, the rest of the thyme and the black pepper. Keep whisking.
Swiftly whisk in two thirds of the beaten eggs and remove from the heat. Quickly thicken with flour or thin with water if necessary. Whisk!
Mix half of the béchamel sauce with half of the pasta and spread across the bottom of a large, deep baking tray. Line up the pasta in 2-3 layers if possible. Add the mince layer and spread evenly. Line up the rest of the pasta on top of the mince and cover with the remaining sauce.
Spread the Parmesan on the top - remember if you add real Parmesan cheese the dish will no longer be vegetarian - you could choose to use a vegetarian substitute hard cheese.
Cook uncovered in a pre-heated oven at 200°C/180°C fan/gas-6 for 30-45 minutes or until the top is browned. Bake long enough to ensure the egg in the mince is fully cooked.
Serve with Egyptian bread, olives and/or your choice of salad.
Adapting the recipe:
Use fresh parsley and thyme if desired - like for like amounts.
Choose full-fat or semi-skimmed milk depending on how creamy you want the sauce, but don't use skimmed milk.
We found a great history of sauces that includes a great section on béchamel here.
And we love the info on this particular dish from The Egyptian Kitchen.