Pat the shrimp dry and cut into smaller pieces.
In a medium mixing bowl, add all the filling ingredients and stir until the ingredients are well mixed together.
Fill a small bowl with water for wetting your fingers.
Hold the wrapper in a diamond shape. Spoon 1 teaspoon of filling in a wrapper. Using the bowl of water, dip your finger then wet the top two sides. Fold the wrapper by bringing one corner over the filling close to the opposite corner, forming a triangle and seal the sides. Twist the bottom corners. Bring the right corner over the wonton, dab some water and bring the left corner on top of the right corner, and press together.
Remaining uncooked wontons can be frozen by placing them in a single layer on a sheet pan. Once frozen, put them in freezer bags. Dumplings do not need to be thawed before cooking and can be cooked using the same instructions.
In a small pot on medium heat, add chicken broth with the shrimp shells, if you have them, ginger and garlic. Bring to a boil, turn down the heat to low and simmer for 10 minutes. Discard the ginger, garlic and shrimp shells. Season with soy sauce and sesame oil.
In a large pot, fill halfway and bring water to a boil. Drop several wontons into the water without overcrowding and cook for 1-2 minutes until the wontons are floating to the top.
Serve wontons in a bowl with broth.