01 - Combine flour, instant yeast, sugar, and salt in a large mixing bowl. Add warm water and olive oil, stirring until a shaggy dough forms. Turn out onto a lightly floured surface and knead for 8 to 10 minutes until smooth and elastic. Transfer to a greased bowl, cover, and let rise in a warm place for 1 hour or until doubled in size.
02 - Preheat oven to 475°F. Line a baking sheet with parchment paper and set aside.
03 - In a medium bowl, combine shredded mozzarella, crumbled feta, diced tomatoes, chopped parsley, dried oregano, and black pepper. Mix thoroughly until evenly distributed.
04 - Punch down the risen dough and divide into 4 equal portions. On a lightly floured surface, roll each piece into an oval shape approximately 10 by 4 inches. Transfer to the prepared baking sheet.
05 - Distribute the cheese and tomato filling evenly over each dough oval, leaving a ½-inch border around the edges. Fold the edges inward slightly and pinch the ends together to create the characteristic boat shape.
06 - Brush the exposed dough edges with melted butter. Bake for 10 minutes until the dough begins to set and lightly brown.
07 - Remove from oven and carefully crack one large egg into the center of each pide. Return to the oven and bake for an additional 7 to 10 minutes until egg whites are fully set while yolks remain slightly runny, and the crust reaches a golden brown color.
08 - Remove from oven and brush edges with additional melted butter if desired. Garnish with chopped fresh parsley. Serve immediately while warm.