For dough: in a large bowl, combine flour, salt, sugar, spices, yeast and milk. Add melted shortening, work with your hands till sandy. Add eggs and enough water to knead into soft elastic dough. Cover and rest in a warm place for 45 minutes till doubled.
For filling: in a pan, heat oil. Brown meat, use a wooden spoon to break all lumps, till liquid evaporates. Take off heat.
In a bowl, pour tahini and add water gradually while mixing with a fork. Add vinegar and seasoning, mix well. Add meat and chives, mix.
On a lightly floured surface, roll dough to 5mm thick. Line in a large greased pan, lifting the dough up the sides. Evenly spread filling, turn dough sides to cover filling edges. Brush filling and dough sides with egg, (arrange tomato slices and chili if desired) and sprinkle sesame. Bake in moderate oven for 30 minutes or till golden. Cool slightly. Cut as desired and serve warm or cold.