In a large bowl, use your hands to combine the pork, green onions, water chestnuts, ginger, garlic, red pepper flakes, soy sauce and sugar.
Place the bowl of filling, the wonton wrappers, a saucer with the beaten egg and a pastry brush on a clean work surface. Have a lightly oiled cookie sheet nearby to hold the dumplings.
Place a scant tablespoon of the filling in the center of each wonton. Brush the beaten egg around the edges of the wrapper. Gather up the corners of the wrapper and pinch them together around the top. Make sure all the edges are sealed. Continue to make the dumplings until the filling is used up. Space them on a large cookie sheet, making sure they don't touch each other.
In a large sauté pan with a lid, heat 1 tablespoon of the oil over medium-high heat. Place the dumplings in the pan so they aren't touching and sauté until they are nicely browned on the bottom. Add 1/2 cup water to the pan and steam the dumplings covered for about 3 minutes, or until pork is cooked through. Repeat the process with the remaining dumplings.
Place the cooked dumplings on a warm platter and serve with the sauce.