Fatayer (Middle Eastern Savory Hand Pies)

Name: Fatayer (Middle Eastern Savory Hand Pies)
Ingredients: 2 cups (454g) water lukewarm; 1 tablespoon (18g) salt; 2 tablespoons (25g) sugar; 2 1/4 teaspoons instant yeast; 1/2 cup (100g) olive oil; 6 cups (720g) King Arthur Unbleached All-Purpo; 1 1/2 cups (170g) feta cheese crumbled; 1 1/2 cups (170g) queso fresco crumbled; 1/4 cup (57g) cream cheese softened; 1 large egg lightly beaten; 1 tablespoon dried oregano; 1 tablespoon dried mint; 1/2 cup (71g) diced onion; 3 cloves garlic; 1 small tomato (about 170g); handful of parsley coarsely chopped; 1 pound (454g) lean ground beef (90% lean preferred); 1 tablespoon Middle Eastern seven spice*; 1 teaspoon allspice*; 1/2 teaspoon salt; 1/4 teaspoon black pepper; 1 1/2 teaspoons chili paste; 1 teaspoon pomegranate molasses; 1 large egg beaten with 1 tablespoon water