Preheat the oven to 350°F. Lightly grease a baking sheet and set aside.
Shred both cheeses on a box grater and put into a mixing bowl. Drizzle in melted butter, parsley, and egg. Stir together until thoroughly combined. Cover and refrigerate until ready to use.
Divide the bread dough into 16 even pieces. Lightly flour a clean work surface. Roll out each piece of dough into a circle about 4” to 5” in diameter.
Spread about 2 tablespoons of the cheese filling down the center of the dough, leaving 1” of edges. Pinch the ends together to create a boat shape, keeping a small 1-inch opening at the center. Transfer to the prepared baking sheet.
Bake the fatayer until lightly browned, about 10 to 12 minutes. Broil for another 30 seconds to 1 minute. Serve warm.
