In a medium bowl, combine ground pork, white parts of scallions, ginger, soy sauce, sesame oil, and cornstarch. Use your hands or a fork to mix until the mixture becomes sticky and paste-like, about 2 minutes. This texture helps the filling hold together when cooked.

Place a wonton wrapper on a clean surface. Add 1 teaspoon of filling to the center. Dip your finger in water and wet two adjacent edges. Fold into a triangle, pressing firmly to seal and pushing out air bubbles. Bring the two bottom corners together, wet one corner, and pinch to seal into a classic wonton shape. Place on a baking sheet and cover with a damp towel. Repeat with remaining wrappers and filling.

In a large pot, bring chicken broth, garlic, star anise, and white pepper to a gentle simmer over medium heat. Let it infuse for 10 minutes, then remove and discard the garlic and star anise. Keep warm over low heat.

Add bok choy to the simmering broth and cook until just tender and bright green, about 3 minutes. Use a slotted spoon to transfer to serving bowls.

Bring a separate pot of water to a boil. Working in batches to avoid crowding, add wontons and stir gently once to prevent sticking. Boil until they float and the wrappers turn slightly translucent, about 4 minutes. Transfer with a slotted spoon directly to serving bowls.

Ladle the hot broth over the wontons and bok choy in each bowl. Garnish with reserved green scallions. Serve immediately while piping hot.