Mix pork, green onions, soy sauce, sesame oil, ginger, egg white, and cornstarch in a bowl.
Keep the wonton wrappers covered with plastic wrap.
Lay out 2–3 wrappers at a time, place a teaspoon of filling in the center, moisten the edges with water, and fold into a triangle.
Moisten the tips, bring them together, and press to seal.
Arrange on a parchment-lined pan or dust the bottoms with flour to prevent sticking.
Bring broth to a boil and add soy sauce, sesame oil, ginger, garlic, carrots, and celery.
Simmer for 2 minutes, then add wontons, bok choy, and broccoli.
Let cook for 5 more minutes, adding shrimp in the last 3 minutes.
Remove from heat, stir in any remaining ingredients, and serve immediately.