Place the flour, water, egg, and salt in a stand mixer bowl and knead using a hook attachment until it's smooth.
Cover the dough with a kitchen towel and let it rest for about 45 mins.
Prepare the Filling:
Mix the ground beef with the onion, black pepper, salt, and chili flakes in a separate bowl. Set aside.
Prepare the Yogurt Topping:
Mix the yogurt with the water, salt and garlic in a bowl. Set aside.
Shape the Manti:
Roll the dough out thinly on a floured surface and cut into small 1/2 inch squares.
Put a pea-sized amount of beef mixture in the center of each square.
Fold the edges from the corners inwards, meeting at the center, and press with your fingertips to obtain a pouch-like shape.
Cook the Manti:
Put the manti inbatches into boiling water. Cook until the manti in batches until they float to the surface, around 4-5 minutes. Then, take them out with a slotted spoon and place them on a serving plate.
Make the Sauce:
Melt the butter in a pan. Add the dried mint and chili flakes. Allow them to sizzle them for a few seconds.
Assembling Manti:
Pour the yogurt mixture over the cooked manti.
Drizzle the sauce over the yogurt-topped manti.
Sprinkle extra red pepper flakes and mint over the top for added flavor.