To rehydrate the glass noodles, in a bowl, cover the dried glass noodles with hot water and soak for about 2 minutes until softened. Drain well and cut into shorter segments.

To cook the vegetables, in a pan over high heat, add the cooking oil. Add the carrot, cabbage, snow peas, and beech mushrooms and stir-fry for about 2 minutes until slightly softened. Add the garlic and stir-fry for about 10 seconds until fragrant. Add the rehydrated glass noodles and season with vegetarian oyster sauce, hoisin sauce, and white pepper. Stir-fry until everything is evenly combined and excess moisture has cooked off. Remove from the heat and let the filling cool slightly.

To assemble the egg rolls, place an egg roll wrapper on a flat surface in a diamond shape with one corner pointing toward you. Spoon about 2 tablespoons of filling near the bottom corner. Fold the bottom corner over the filling, fold in both sides, and roll tightly. Brush the top corner with beaten egg to seal. Repeat with the remaining wrappers and filling.

To fry the egg rolls, in a pot over high heat, add cooking oil and heat to 350°F (177°C). Carefully add the egg rolls in batches and fry for about 4 minutes, turning as needed, until golden brown and crispy. Remove and drain on a rack.

Serve hot with your favorite dipping sauce.