Drain and rinse your bean sprouts. The wrappers should be 7 inches.
Rehydrate the oriental mushrooms in hot water for 30 minutes.
Toss the carrot with 1 tsp sugar until mixed then let sit tossing occasionally for 15 minutes.
Drain the mushrooms save 1/2 cup of the liquid. Squeeze excess water out of the mushrooms then cut off stems and cut caps into thin slices.
Heat the wok over med high. When hot drizzle 2 tbsp oil into it and heat for 30 seconds. Add the onion and stir fry for a minute. Then add the mushrooms, garlic and liquid reducing heat to medium. Cover and cook about 3 minutes. Mushrooms should be tender. Uncover add the soy sauce and sesame oil and sugar.
Cook and stir mushroom mixture 3 to 5 minutes more or until all liquid has evaporated. Transfer mushroom mixture to medium bowl; set aside to cool slightly. Cook stirring for about 4 minutes. Liquid should be gone. Then set aside in bowl to cool. Add the carrot strips and bean sprouts to mix and toss lightly.
Place a wrapper on surface and keep rest covered. Drain mushroom mix and place 3 tbsp on wrapper's bottom 3rd. Brush edges with beaten egg.
Now: Fold bottom corner up over filling.
Fold in and overlap the opposite right and left corners to form 3-1/2-inch-wide log. Roll up filling to remaining corner and place spring roll on tray covered with plastic wrap. Repeat with remaining wrappers and filling.
Now take the remaining 3 cups of oil, place in wok and heat. You want 375F on a deep fry thermometer. Fry 4 rolls 2 to 3 minutes or until golden brown.
Reheat oil and do next batch. Repeat until all are used. Drain on paper towels. Place on serving tray with dipping sauce. Serve.