01 - Mix flour, instant yeast, sugar, and salt in a large bowl. Add warm water and olive oil. Stir 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 - Combine mozzarella, feta, tomatoes, parsley, oregano, and black pepper in a bowl. 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 boat shape.
06 - Brush dough edges with melted butter.
07 - Bake for 10 minutes.
08 - Remove from oven and carefully crack an egg into center of each pide. Return to oven and bake for 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.