Prepare the Wonton Filling:

1. Mix Filling: In a bowl, combine the ground pork, green onions, soy sauce, sesame oil, grated ginger, minced garlic, salt, and pepper. Mix well until the ingredients are thoroughly combined.

Fill and Fold the Wontons:

1. Assemble Wontons: Place a teaspoon of the pork mixture in the center of each wonton wrapper. Moisten the edges of the wrapper with water, fold in half to form a triangle, and press the edges to seal. For a more traditional shape, bring the two opposite corners together, dab with a little water, and press to seal. Repeat with the remaining wrappers and filling.

Cook the Wontons:

1. Boil Wontons: Bring a large pot of water to a boil. Add the wontons in batches, making sure not to overcrowd the pot. Cook for about 4-5 minutes, or until they float to the top and the filling is cooked through. Remove with a slotted spoon and set aside.

Prepare the Soup:

1. Simmer Broth: In a separate pot, combine the chicken or vegetable broth, water, soy sauce, sesame oil, and ginger slices. Bring to a simmer over medium heat. Simmer for about 10 minutes to infuse the broth with the ginger flavor. Remove the ginger slices with a slotted spoon and discard.
2. Assemble the Soup: Add the cooked wontons to the simmering broth. If using, add the additional garnishes like bok choy or mushrooms, and cook for another 2-3 minutes, or until the vegetables are tender. For leafy greens like spinach, you can just stir them in at the last minute until wilted.
3. Serve: Ladle the soup and wontons into bowls. Garnish with chopped green onions and a drizzle of sesame oil, if desired.