In a mixing bowl, combine the flour and salt. Create a well in the center and add the egg. Gradually mix in water until a dough forms. Knead the dough on a floured surface for about 5 minutes until smooth. Cover and let it rest while preparing filling and soup.
In another bowl, mix the cooked chicken or pork, green onions, soy sauce, and ginger. This will be your dumpling filling.
Roll out the dough on a floured surface until it's about 1/8 inch thick. Cut into 3-inch circles using a knife or a round cutter.
Place a teaspoon of the filling in the center of each circle. Fold the dough over and pinch the edges to seal. Repeat until all dumplings are formed.
In a large pot, heat the oil over medium heat. Add the minced garlic and sauté until fragrant, about 1 minute.
Pour in the broth and bring to a boil. Add the sliced carrots and simmer for 5 minutes.
Carefully drop the dumplings into the boiling broth and cook for about 10-12 minutes until they rise to the surface and are cooked through.
Stir in the bok choy or spinach, and let simmer for an additional 3-5 minutes until wilted. Season with salt and pepper to taste.
Serve hot, garnished with fresh herbs if desired.