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 dough and divide into 4 equal pieces. Roll each into an oval about 10 x 4 inches.
05 - Transfer ovals to prepared baking sheet. Spread cheese and tomato mixture evenly over each, leaving a ½-inch border. Fold edges over slightly and pinch ends to form a boat shape.
06 - Brush dough edges with melted butter.
07 - Bake for 10 minutes. Remove from oven and carefully crack an egg into the center of each pide.
08 - Return to oven and bake for another 7–10 minutes, until egg whites are set but yolks remain slightly runny and edges are golden.
09 - Remove from oven, brush edges with more melted butter if desired, and garnish with parsley. Serve warm.