In a mixing bowl, combine the ground pork, green onions, soy sauce, sesame oil, garlic, and ginger. Mix well until all ingredients are evenly incorporated.
Take a wonton wrapper and place about 1 teaspoon of the pork mixture in the center. Moisten the edges of the wrapper with water, fold it in half to form a triangle, and press the edges to seal. Bring the two corners of the triangle together to form a little pouch and press to seal. Repeat with remaining wrappers and filling.
In a large pot, bring the chicken broth to a simmer over medium heat. Add the sliced mushrooms and cook for about 5 minutes.
Gently add the wontons to the simmering broth. Cook for about 5-7 minutes or until the wontons float to the surface and are cooked through.
Stir in the chopped bok choy and additional soy sauce. Cook for another 2-3 minutes until the bok choy is tender. Season with salt and pepper to taste.
Ladle the soup into bowls and garnish with chopped cilantro if desired. Serve hot.