For the shrimp dumplings

1. Make filling. Pat dry the shrimp with paper towels and roughly chop. Place the shrimp in a medium bowl and stir in the green onions, sesame oil, salt, and pepper. Sprinkle in the cornstarch and mix until evenly combined.
2. Fold dumplings. Lay 6-7 dumpling wrappers on a clean work surface. Scoop 1 teaspoon of shrimp filling on each wrapper. Brush the edges of the wrappers with water and fold the wrappers in half to create a semi-circle. Press firmly around the edges to ensure a good seal pushing out any air as you go. Then brush the folded edges of each dumping with more water and fold in the two sides. Press to seal. Lay the dumplings on a plate and cover loosely with a clean towel or some wax paper. Repeat with the remaining wrappers and filling. You will have some extra filling leftover which will be used in the soup broth.

For the soup broth

1. Simmer broth. Heat sesame oil in a large saucepan over medium-high heat. Add green onions and leftover shrimp filling and cook until shrimp is mostly cooked through. Stir in chicken broth scraping up any browned bits from the bottom of the pan. Add ginger, soy sauce, and Chinese cooking wine. Bring broth a boil then reduce heat and simmer for 8-10 minutes.
2. Cook dumplings. Remove ginger pieces and add half of the dumplings. Cook dumplings for 3 minutes. Using a slotted spoon, remove the dumplings from the broth and evenly divide them into two serving bowls. Repeat with the remaining dumplings.
3. Serve. Taste the broth and season to taste with salt as needed. Ladle the soup broth into the serving bowls. Garnish with additional green onions, if desired.