Each of these tiny dumplings is about the size of your fingertip, so you can easily serve 20 to 25 to each person. It's traditional to invite two or three friends to help fill and seal the manti; after all, many hands make light work.
Make the dough: Sift together flour and salt in a large bowl. Make a well in center, and add egg. Using your hands, gently draw flour mixture into egg. Gradually add the cold water, and continue to work dough with your hands or a spoon until it forms a smooth mass.
Turn dough onto a lightly floured surface. Knead until dough is smooth and springs back when pressed, 5 to 8 minutes. Divide dough into 2 balls, cover with a damp kitchen towel, and let rest at room temperature for 30 minutes.
Make the filling: Gently combine lamb, onion, parsley, salt, and pepper. (Filling can be refrigerated in an airtight container for up to 2 days.)
On a lightly floured work surface, roll out 1 portion of dough into a 16-by-10-inch oblong about 1/16 inch thick. Using a ruler, cut dough into 1 1/4-inch squares with a pizza wheel or a paring knife. Keep remaining dough covered with a damp kitchen towel while you work.
Spoon 1/4 teaspoon filling in center of 1 dough square. Gently pull 2 opposite corners outward to stretch dough slightly, then pull up to meet in center, and pinch to seal. Repeat with remaining 2 corners, making sure all air has been pressed out. Pinch together all 4 corners to form a point, then pinch along all 4 seams to seal. Place on a parchment-lined baking sheet, and cover with a damp kitchen towel. Repeat. Remove towel, and cover with a piece of parchment. (Dumplings can be refrigerated on baking sheets, wrapped in plastic, for up to 1 day. Alternatively, freeze on baking sheets, uncovered, for 2 hours, then transfer to an airtight container and freeze for up to 1 month.)
For cooking and serving: Preheat oven to 400 degrees. Coat a 13-by-9-inch baking dish with 1 tablespoon butter. Arrange manti in a single snug layer in dish. Bake until fragrant and tops and corners are golden brown, about 25 minutes.
Meanwhile, bring stock, cinnamon, bay leaves, and 1 teaspoon salt to a boil in a saucepan. Remove baking dish from oven, and add enough stock mixture to dish so that all but the tops of manti are submerged. Cover tightly with parchment and then foil, and bake until soft, about 25 minutes more.
Meanwhile, stir together yogurt or labneh and garlic paste in a medium bowl. When manti have finished cooking, tilt baking dish, collect about 1/4 cup liquid with a ladle, and stir into yogurt sauce (sauce should be spoonable).
Melt remaining 7 tablespoons butter in a small saucepan over medium-high heat. Reduce heat to medium, and cook until amber, about 7 minutes.
Divide manti among shallow serving bowls. Spoon yogurt sauce over top, drizzle with browned butter, and sprinkle with mint and red pepper.
Manti can be frozen for up to 1 month.