In a large bowl, combine: ground beef, ginger, garlic, curry powder, soy sauce cornstarch, salt, sesame oil, just ONE of the eggs, bell pepper and green onion. Mix thoroughly.
In a small bowl, combine the final egg and 1 tablespoon water and whisk to make the egg wash.
Place one wonton wrapper in your hand or flat on the table. Lightly brush a thin layer of the egg wash around the edges of the wrapper. Scoop 1 tablespoon of the beef mixture into the center of the wrapper. Pull the sides of the wrapper up and push together slightly to stick to the meat mixture. The bottom of the dumpling should be flat so it can stand up in the pan.
Repeat until all the wrappers and filling are used up, making sure to cover any finished dumplings and the unused wrappers with plastic wrap or a barely damp towel to keep them from drying out.
Dumplings can be cooked immediately or frozen for up to 1 month. If freezing, make sure they are not touching when they are first frozen, then once they're frozen, they can be gathered together and stored in a freezer bag.
To cook, in a large nonstick sauté pan or skillet, heat 1 tablespoon of cooking oil over medium heat. Add dumplings to the pan, making sure they are not too crowded. Cook for about 2 minutes, or until the bottoms are lightly browned.
Once the bottoms are browned, it's ready to finish cooking them by steaming. Hold the sauté pan lid (like a shield) to protect you from splatters. Carefully pour in 3-4 tablespoons of water into the pan and immediately cover. Turn heat down to medium-low and let the dumplings steam until they are cooked through and the water has mostly evaporated. This should take about 2 minutes.
Transfer the cooked dumplings to a plate and tent with a piece of foil to keep them warm. Repeat with the remaining dumplings. Serve immediately.