In a mixing bowl, combine flour, salt, sugar, and yeast.

Add warm water and olive oil, and mix until a dough forms.

Knead the dough for about 10 minutes until smooth.

Let the dough rise in a warm place for 1 hour.

In a bowl, mix feta and mozzarella cheese together.

Preheat the oven to 450°F (230°C).

Divide the dough into 4 equal pieces and roll each into a circle.

Place cheese filling in the center of each circle and fold the edges over the filling.

Place on a baking sheet and bake for 20-25 minutes until golden brown.

Remove from oven and brush with beaten egg for a glossy finish.