In a small bowl, dissolve yeast in warm milk. Let it sit for 10 minutes until frothy.
In a large mixing bowl, combine flour, sugar, mahlab, mastic, and salt.
Add the yeast mixture, eggs, melted butter, and vanilla extract to the dry ingredients. Mix until a dough forms.
Knead the dough on a floured surface for about 10 minutes until smooth and elastic.
Place the dough in a greased bowl, cover with a damp cloth, and let it rise in a warm place for about 1.5 hours or until doubled in size.
Preheat the oven to 350°F (175°C). Punch down the dough and divide it into three equal parts. Braid the dough and place it on a baking sheet.
In a small bowl, whisk together the egg yolk and water. Brush the egg wash over the braided dough.
Bake for 25-30 minutes or until golden brown. Let it cool on a wire rack before serving.