Prepare the Dough: In a stand mixer bowl, combine flour, yeast, sugar, and salt. Add warm water, warm milk, and olive oil. Knead using the dough hook for 5-7 minutes, until a soft dough forms. If sticky, add more flour, 1 tbsp at a time.
Let It Rise: Lightly coat the dough ball with oil, cover with a towel, and let it rise for 1 hour in a warm place.
Make the Cheese Filling: While the dough rises, mix mozzarella, feta, parsley, and mint in a bowl.
Divide and Shape: Once the dough has doubled in size, divide it into 12 equal pieces (or 18 for mini fatayer). Shape each into a ball, cover, and let rest for 10 minutes.
Roll Out: Preheat the oven to 400°F (205°C). Roll each dough ball into a ¼-inch thick circle. Place on a parchment-lined baking sheet. Flip each circle sticky side up to help seal the fatayer better.
Fill and Shape: Place 1-2 tbsp of cheese mixture in the center of each dough circle. Pinch opposite sides together to form a diamond or boat shape, ensuring the edges are sealed well.
Egg Wash & Garnish: Brush the edges with beaten egg and sprinkle with sesame seeds.
Bake: Bake for 10-12 minutes or until golden brown and the cheese is melted.
Serve Warm: Enjoy with a side of yogurt or fresh salad.