Mix the flour and salt. Add the egg and most of the water, then knead for 8 to 10 minutes, adding the remaining water only as needed for a firm, smooth dough.
Cover and rest the dough for 30 minutes.
Fill and Shape:
Combine the beef, onion, parsley, salt, and pepper. Divide the dough into four pieces, keeping the rest covered.
Roll one piece very thin and cut into roughly 1-inch squares. Put about 1/4 teaspoon filling in each square, bring the corners together, and pinch firmly. Repeat on a floured tray.
Cook and Serve:
Stir the yogurt, garlic, and salt together. Melt the butter in a small saucepan, add the Aleppo pepper, and cook gently for 30 seconds.
Boil the manti in well-salted water for 8 to 10 minutes until tender, then drain. Spoon into bowls and top with garlic yogurt, pepper butter, and dried mint.
Notes
Use only a small amount of filling so the seams close securely.
If the yogurt is very cold, let it stand briefly at room temperature so it does not cool the dumplings too quickly.