First, prepare the meat mixture. In a large frypan heat the Olive oil, add onion
and garlic and sauté for about 5 minutes. Add the tomato paste and mince and
sauté for another 5 minutes. Add the crushed tomatoes and All spice. Season to
taste with salt and pepper. Allow the sauce to simmer uncovered for 15 minutes
so that excess liquid can evaporate.

Melt butter over low heat. Using a whisk, add flour
whisking continuously to make a smooth paste. Add warmed milk to mixture
whisking continuously. Simmer over low heat until it thickens a bit but does not
boil, stirring continuously. Remove from heat and stir in the beaten egg, and a
pinch of nutmeg. Add the cheese and continue to stir for another minute. Return
to heat and stir until sauce thickens.

Meanwhile, boil the pasta in plentiful salted water and drain thoroughly. Place
the pasta in a oven dish and sprinkle with the rest ½ cup of grated cheese and
toss. Cover the pasta with a layer of meat sauce and on top pour the béchamel.

Bake the pastitsio at 180°C for approximately 1 hour until the surface is golden
brown. Let it cool down for a while to set. Cut into large rectangular pieces and
serve.