For the wonton filling: Place the shrimp, pork, 1 teaspoon salt, 1/2 teaspoon pepper, the oyster sauce and sesame oil in a medium bowl and mix with your hands to combine. Let marinate while you prepare the stock. (If time allows, marinate for at least 20 minutes and up to overnight; refrigerate if marinating for more than 2 hours.)
For the broth: Bring 2 quarts water to a simmer in a large saucepan or pot and whisk in the chicken base until completely dissolved. Add the remaining broth ingredients and let simmer for at least 5 minutes.
Continue making the wontons: Bring a large pot of salted water to a boil. Place about 1 teaspoon of the filling in the center of 1 wonton wrapper. Moisten the edges with some of the beaten egg. Pinch in all the sides to make a small sack, enclosing the filling. Transfer to a plate. Repeat with the remaining filling and wrappers.
For the noodles: Add the noodles to the boiling water and cook according to the package directions. During the last 3 to 5 minutes of cooking time, add the wontons and continue to boil until the wontons are cooked through and float to the top. Drain the noodles and wontons.
For the assembly: Ladle 2 cups of the broth into each of 4 deep bowls. Divide the noodles and wontons among the bowls. Garnish with the scallions and cilantro.