In a mixing bowl, combine ground beef or chicken with soy sauce, sesame oil, and rice vinegar. Add garlic, ginger, green onions, and pepper. Mix until evenly combined.
Lay a wonton wrapper flat on a clean surface. Place a small spoonful of filling in the center. Moisten edges with water, fold into a triangle, pressing edges tightly to seal. Bring the two bottom corners together and press to seal. Repeat with remaining wrappers.
In a large pot, bring chicken broth to a boil. Add soy sauce, sesame oil, ginger slices, and green onions. Optional: add bok choy, simmer on low for 10-15 minutes to blend flavors. Carefully drop wontons into the simmering broth. Cook for 3-5 minutes, or until they float to the surface. Remove ginger slices before serving for a smoother texture.
Ladle soup into bowls, ensuring each bowl has several wontons. Garnish with green onions or bok choy if desired. Season with salt and pepper to taste, and serve hot.