To prepare the glass noodles and sauce, in a bowl, soak the glass noodles in hot water until softened, about 4 minutes. Drain and cut into 1-inch segments. In a separate bowl, combine the soy sauce, oyster sauce, hoisin sauce, white pepper, and cornstarch slurry, then whisk until well combined.
To cook the filling, in a pan over high heat, add 1 tablespoon of cooking oil. Add the ground chicken and salt, then stir-fry for 2 minutes. Remove and set aside. In the same pan, add the remaining tablespoon of cooking oil. Add the carrot, shiitake mushrooms, cabbage, snow peas, and garlic, then stir-fry until aromatic, about 1 minute. Return the chicken to the pan along with the glass noodles and sauce. Stir everything together, then let the filling cool for about 10 minutes before wrapping.
To assemble the spring rolls, place a spring roll wrapper on a flat surface like a diamond, with a corner pointing toward you. Spoon about 2 tablespoons of filling near the bottom corner. Fold up the bottom corner, then fold in the sides. Roll tightly but not too tight. Brush the top corner with the egg wash and seal. Repeat with the remaining wrappers.
To fry the spring rolls, in a deep pot, heat the cooking oil to 350°F (177°C). Fry the spring rolls in batches for about 3 minutes, or until golden brown and crispy. Transfer to a wire rack or paper towel-lined plate to drain excess oil.
To serve, enjoy the spring rolls as-is or pair them with sweet and sour sauce.