Mix flour, salt, yeast, sugar, yogurt, olive oil, and lukewarm water in a bowl. Knead for 2–3 minutes until smooth. Add flour 1 tbsp at a time if sticky.
Place dough in an oiled bowl, cover, and let rise in a warm spot for 1 hour or until doubled.
Combine mozzarella, feta, parsley, egg, and all seasonings in a bowl. Mix well and set aside.
Preheat oven to 475°F. Punch down dough and divide into 12 balls. Roll each into a 5-inch oval.
Add 1 tbsp filling to each oval. Fold sides over and pinch ends to form a boat shape.
Place on a parchment-lined tray, brush edges with milk or cream. Bake for 10–12 minutes until golden.
Let cool a few minutes before serving. Enjoy warm with melty cheese inside.