01 - In a spacious mixing bowl, combine shredded chicken breast, buffalo wing sauce, mozzarella cheese, blue cheese, celery, green onions, garlic powder, and black pepper. Blend thoroughly until the ingredients are evenly incorporated.
02 - Position one egg roll wrapper on a clean work surface with a corner facing you. Place 2 to 3 tablespoons of chicken filling in the center. Fold the bottom corner over the filling, tuck in both sides, and roll tightly. Lightly brush the top corner with beaten egg to ensure a secure seal.
03 - Continue filling, folding, and sealing the remaining egg roll wrappers with the prepared mixture.
04 - Pour approximately 2 inches of vegetable oil into a deep-frying pot or heavy-bottomed Dutch oven. Preheat the oil to 350°F using a kitchen thermometer for accuracy.
05 - Working in batches, carefully lower egg rolls into the hot oil. Fry each batch for 3 to 4 minutes, turning occasionally, until the exterior is golden brown and crisp. Transfer immediately to a plate lined with paper towels to drain excess oil.
06 - Arrange the hot egg rolls on a platter and present with ranch or blue cheese dressing for dipping if desired.