Make the broth base: In a large pot, combine chicken broth, sliced ginger, smashed garlic, and the white parts of the scallions.
Bring to a simmer over medium heat and cook for 15–20 minutes to infuse.
Season the broth: Remove the ginger and garlic with a slotted spoon. Stir in soy sauce, rice vinegar, sesame oil, and a pinch of white pepper. Taste and adjust salt or soy as needed.
Keep at a gentle simmer.
Mix the filling: In a bowl, combine ground pork, chopped shrimp, soy sauce, Shaoxing wine, grated ginger, minced garlic, scallions, sesame oil, cornstarch, and a pinch of salt and white pepper. Stir until slightly sticky and well combined.
Fill the wontons: Place 1 teaspoon of filling in the center of a wonton wrapper. Moisten two edges with water, fold into a triangle, press to seal, then bring the two bottom corners together and pinch.
Keep covered with a damp towel so they don’t dry out.
Add vegetables to the broth: Stir in bok choy, mushrooms, and carrots. Simmer 3–4 minutes until just tender but still vibrant.
Cook the wontons: Gently slide 10–14 wontons into the simmering broth (work in batches to avoid overcrowding). Cook 3–5 minutes, or until the wontons float and the filling is cooked through.
Finish and serve: Ladle broth, vegetables, and wontons into bowls.
Top with the green parts of the scallions, a drizzle of chili oil, and fresh cilantro. Add a squeeze of lime if you like brightness.