Combine yeast cube into luke warm milk. Stir 1 t sugar and let it stand to proof until bubbly and doubled in volume, about 10 minutes.
Mix butter, olive oil, the rest of the sugar and eggs, beat well.
Add flour, the rest of the milk, mastic powder, mahlab powder to the egg mixture. Finally add the yeast and knead well.
Make a soft dough. Dough will stick to the bowl, but should not stick to your fingers.
If you are kneading by hand; turn out onto a well-floured surface and knead about 10 minutes by using only enough flour necessary to prevent sticking to your hands.
Transfer the dough to a large bowl. Cover with a tea towel and let rise in a warm place, about 2 hours or until double in volume.
Cut dough into 12 equal pieces. You can weight each piece of dough to have equal piece of dough.
Make 20 cm long strips from doughs and put together 4 of them to make a braid.
Place each braid in a buttered or parchment paper covered baking tray. Allow them to rise for 30 minutes.
For the top:
Beat together 1 egg yolk with 1 t milk.
Generously brush the top and sides of the bread with the egg mix just before baking.
Bake them in 190° C pre-heat oven until golden brown for about 20- 30 minutes.