In a large mixing bowl, combine the flour, sugar, yeast, and salt. Mix thoroughly to ensure even distribution of dry ingredients. In a separate bowl, whisk together yoghurt, milk, and oil until smooth. Gradually pour the wet mixture into the dry ingredients, stirring with a spoon or your hands until a soft dough forms. Knead briefly until smooth. Cover with a damp cloth and let it rise in a warm spot for about 1 hour or until doubled in size.
While the dough is rising, prepare the filling. In a bowl, grate the haloumi cheese and finely chop the parsley. Mix well to combine, creating a savory, aromatic filling. You can add a pinch of salt or extra herbs if desired. Set aside once ready.
Once the dough has risen, punch it down gently. Divide into 8-10 equal portions. Roll each portion into a thin circle, about 15-20cm in diameter. Place a generous spoonful of cheese filling in the center of each circle. Fold the dough over the filling to create a semi-circle or shape into a pouch, pinching the edges together firmly to seal.
Preheat your oven to 200°C (392°F). Line a baking sheet with parchment paper. Place the filled fatayer on the prepared sheet, spacing them apart. Bake for 15-20 minutes, or until golden brown and crispy on the edges. Remove from oven and serve warm for the best flavor and texture.