Mix ground pork, minced ginger, garlic, green onions, soy sauce, sesame oil, and white pepper in a bowl until combined well.
Put 1 teaspoon of filling in the middle of each wonton wrapper, wet the edges with water, and fold into a triangle.
Bring the triangle corners together and press hard to seal, making the classic wonton shape with no air pockets inside.
Heat chicken broth with ginger slices, soy sauce, and sesame oil in a large pot over medium-high heat until it starts bubbling.
Turn the heat down to medium and let the broth simmer for 10 minutes so all the flavors mix together really well.
Drop wontons into the simmering broth one at a time and cook for 6 to 8 minutes until they float up.
Add chopped bok choy during the last 2 minutes of cooking, letting the greens wilt but still stay a bit crisp.
Scoop wontons and broth into bowls, top with sliced green onions and a drizzle of sesame oil, then serve right away.
