Cut the green and white parts of the green onions into thin slices. Place in a medium bowl. Add the drained corn, sesame oil, ginger, and soy sauce to the bowl.
Chop the shrimp into small pieces and add to the bowl. Stir until combined.
Fill a small bowl with water. Place a won ton wrapper in your hand and add a small amount of filling (about ½ tablespoon). Use your fingers to wet the edges of the wrapper. Fold diagonally and pinch the edges to seal. Then squeeze the two far corners of the triangle together to make a half-moon shape. Set aside and continue until you've used up the filling.
Once all of the dumplings are prepared, heat about 2 tablespoons vegetable oil in a large nonstick saute pan over medium heat.
Add half of the dumplings in a single layer. Cook for 2 to 3 minutes until a golden crust forms on the bottom. Then add vegetable broth to the bottom of the pan and cover.
Cook for another 2 to 4 minutes until the dumplings are glossy and slightly translucent. When you think they're ready, take one out of the pan, cut in half, and make sure the shrimp is fully cooked through.
Move the dumplings to a plate and cook the rest of the dumplings using the same steps.
Serve the dumplings with the Zhenjiang vinegar as a dipping sauce.