01 - In a large bowl, thoroughly combine shredded chicken, buffalo wing sauce, mozzarella cheese, blue cheese, celery, green onions, garlic powder, and black pepper until the mixture is evenly coated.
02 - Position an egg roll wrapper on a clean, dry work surface with one corner facing you. Add 2 to 3 tablespoons of filling onto the center of the wrapper.
03 - Fold the bottom corner over the filling, then fold in the two sides. Roll tightly toward the top corner, brushing the remaining corner with beaten egg to ensure a secure seal.
04 - Continue with the remaining wrappers and filling, keeping completed egg rolls covered with a damp towel to prevent drying.
05 - Pour 2 inches of vegetable oil into a deep, heavy-bottomed pot and heat to 350°F.
06 - Working in batches, fry egg rolls for 3 to 4 minutes each until golden brown and crisp. Remove with tongs and drain on paper towels.
07 - Serve the egg rolls warm with ranch or blue cheese dressing for dipping.