Reduce heat to medium and add the leek, onion, mushrooms, thyme, bay leaves, allspice, and eggplant.
Stir until vegetables are soft, about 3-5 minutes, and add the tomatoes, wine, sugar, salt, and pepper.
Reduce heat to low, cover the pan and simmer until the liquids are evaporated about 20-30 minutes.
Lightly brush them with some olive oil. Keep in mind that the filling already has some oil and fat, so don’t use much.
Continue with all the phyllo, reserving 4-5 sheets for the top. Remember to lightly brush each layer with oil.
Fill the pan with the minced meat mixture and fold the overhanging phyllo sheets over the filling.
Cover the filling with one sheet of phyllo, brush with olive oil and repeat with the rest.
Brush the top with a bit of olive oil and score the surface into squares.
Sprinkle with sesame and 2 tablespoons water.
Let the pie rest for 20 minutes before cutting.