01 - Combine flour, instant yeast, sugar, and salt in a large bowl. Add warm water and olive oil, stirring until a shaggy dough forms. Knead for 8–10 minutes until smooth and elastic. 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.
03 - In a bowl, combine mozzarella, feta, tomatoes, parsley, oregano, and black pepper. Set aside.
04 - Punch down the dough and divide into 4 equal pieces. Roll each into an oval about 10 x 4 inches.
05 - Transfer ovals to the prepared baking sheet. Spread the cheese and tomato mixture evenly over each, leaving a ½-inch border. Fold the edges over slightly and pinch the ends to form a boat shape.
06 - Brush the dough edges with melted butter.
07 - Bake for 10 minutes. Remove from oven and carefully crack an egg into the center of each pide. Return to oven and bake for another 7–10 minutes, until egg whites are set but yolks remain slightly runny and edges are golden.
08 - Remove from oven, brush edges with additional melted butter if desired, and garnish with parsley. Serve warm.