Grate pecorino and halloumi into a bowl and mix flour, semolina, yeast, mint, and sultanas in another.
Combine the dry mixture, cheese, beaten eggs, and milk by hand, then cover and set aside.
Mix pastry flour, mastic, mahlepi, sugar, salt, yeast, butter, and 350ml milk into a soft dough.
Knead the dough on a floured surface until smooth, then let it rest covered for 1 hour.
Boil sesame seeds in water and vinegar, drain, and dry them on a tea towel.
Preheat oven to 200°C and line three baking trays with parchment paper.
Roll dough to 3mm thick and cut into twelve 15cm rounds, pressing one side into sesame seeds.
Add baking powder to the filling and place portions into the center of each dough circle.
Fold into triangles with exposed centers, glaze with egg yolk, and bake at 200°C for 15 minutes.
Lower heat to 180°C and bake for another 15 minutes until golden brown.