01 - Combine shredded chicken, buffalo wing sauce, mozzarella cheese, crumbled blue cheese, celery, green onions, garlic powder, and black pepper in a large mixing bowl. Mix thoroughly until evenly incorporated.
02 - Lay an egg roll wrapper on a clean work surface with a corner facing you. Place 2 to 3 tablespoons of filling in the center. Fold the bottom corner over the filling, fold in the sides, and roll tightly. Brush the top corner with beaten egg to seal.
03 - Repeat the rolling process with remaining wrappers and filling until all egg rolls are prepared.
04 - Pour approximately 2 inches of vegetable oil into a heavy-bottomed pot or deep-fryer and heat to 350°F.
05 - Fry egg rolls in batches for 3 to 4 minutes per batch, turning as needed, until golden brown and crisp. Remove and drain on paper towels.
06 - Serve the egg rolls warm with ranch or blue cheese dressing for dipping.