Divide the dough in half. Place one half on a lightly floured surface and keep the other covered.
Roll the dough into a thin sheet. Use a 4 inch (10 centimeter) round cutter to cut out circles of dough as close together as possible (any scraps will be difficult to roll back out).
Place about 1 tablespoon of the prepared cheese filling in the center of a circle.
Brush the edges of the circle with water and fold over the filling to form a crescent or half moon shape.
Pinch together the edges, pushing out any air from the filling.
Use the tines of a fork to press the edges completely to seal.
Gently press down on the pie with your hand or a rolling pin to keep the filling in a thin layer without any of it bursting out.
Repeat with the remaining circles and filling, rolling out the other half of the dough and cutting out more circles.
Add about 1 inch (2.5 centimeters) of olive oil or sunflower oil to a medium pan and place over medium heat.
Once heated, add a few of the prepared pies in a single layer in the pan.
Cook until golden, then gently flip to cook the other side until golden.
Remove to towel-lined plate and repeat with the remaining pies.
Serve the Pitarakia Milou warm or cold.