01 - In a large mixing bowl, combine shredded chicken, buffalo wing sauce, mozzarella cheese, blue cheese, celery, green onions, garlic powder, and black pepper. Mix until all ingredients are well incorporated.
02 - Place an egg roll wrapper on a flat surface with a corner facing you. Spoon 2 to 3 tablespoons of the chicken mixture onto the center of the wrapper.
03 - Fold the bottom corner over the filling, then fold in the sides, and roll tightly towards the opposite corner. Brush the top corner with the beaten egg to seal the roll securely.
04 - Continue filling, rolling, and sealing the remaining wrappers until all of the chicken filling is used.
05 - In a deep pot or deep fryer, heat 2 inches of vegetable oil to 350°F (175°C).
06 - Working in batches, carefully add egg rolls to the hot oil and fry for 3 to 4 minutes, turning occasionally, until golden brown and crisp. Remove with tongs and drain on paper towels.
07 - Serve egg rolls warm, accompanied by ranch or blue cheese dressing for dipping.