In a bowl, mix pork, soy sauce, sesame oil, ginger, garlic, green onion, cornstarch, and white pepper.
Stir vigorously until the mixture becomes sticky (about 2 minutes).
Place 1 tsp of filling in the center of a wonton wrapper.
Dip your finger in water and moisten the edges.
Fold into a triangle, press to seal, then bring the two corners together and pinch to form a classic wonton shape. Repeat for all.
Bring a pot of water to a boil. Gently drop in wontons (in batches) and cook for 3-4 minutes until they float. Remove with a slotted spoon.
In a separate pot, simmer stock with ginger, garlic, soy sauce, and sesame oil for 10 minutes. Strain if desired.
Divide cooked wontons into bowls. Ladle hot broth over them.
Garnish with green onions and leafy greens. Serve immediately!