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 to 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 - Mix mozzarella, feta, tomatoes, parsley, oregano, and black pepper in a bowl until evenly combined. Set aside.
04 - Punch down risen dough and divide into 4 equal portions. Roll each piece into an oval approximately 10 x 4 inches.
05 - Transfer dough ovals to prepared baking sheet. Spread cheese and tomato mixture evenly over each oval, leaving a ½-inch border. Fold edges over slightly and pinch ends to create boat shapes.
06 - Brush dough edges with melted butter.
07 - Bake for 10 minutes. Remove from oven.
08 - Carefully crack an egg into the center of each pide. Return to oven and bake for 7 to 10 minutes longer, until egg whites are set but yolks remain slightly runny and edges are golden brown.
09 - Remove from oven, brush edges with additional melted butter if desired, and sprinkle with chopped parsley. Serve warm.