In a bowl, mix the flour, egg, and water to form a soft dough. Let it rest for about 15 minutes.
Heat the vegetable oil in a large pot over medium-high heat.
Add the chopped onion and minced garlic, and sauté until softened and fragrant.
Add the beef or lamb pieces to the pot and cook until browned.
Stir in the sliced carrots and cubed potato. Cook for a few minutes.
Pour in the water or beef broth. Add the soy sauce, salt, and ground black pepper. Bring to a boil.
Reduce the heat to low, cover, and let it simmer for 20-30 minutes, or until the meat and vegetables are tender.
Roll out the dough on a floured surface to about 1/4-inch thickness.
Cut the dough into small squares or circles.
Gently drop the dough pieces into the simmering soup. Cook for another 10 minutes or until the dumplings are cooked through.
Garnish with fresh herbs if desired.
Enjoy your meal!