01 - In a large bowl, mix shredded chicken breast, buffalo wing sauce, mozzarella cheese, blue cheese, celery, green onions, garlic powder, and black pepper until evenly combined.
02 - Lay an egg roll wrapper on a clean surface, oriented with one corner pointing toward you.
03 - Spoon 2 to 3 tablespoons of chicken filling into the center of the wrapper.
04 - Fold up the bottom corner over the filling, fold in both side corners, and roll tightly. Brush the top corner with beaten egg to seal the roll.
05 - Continue filling, rolling, and sealing with the remaining wrappers and chicken mixture.
06 - Pour vegetable oil into a deep-frying pot or deep-fryer to a depth of about 2 inches and heat to 350°F.
07 - Working in batches, fry the egg rolls for 3 to 4 minutes until golden brown and crisp. Remove with tongs and drain on paper towels.
08 - Serve the egg rolls warm with ranch or blue cheese dressing on the side for dipping.