01 - In a large mixing bowl, combine shredded chicken breast, buffalo wing sauce, mozzarella cheese, blue cheese if desired, celery, green onions, garlic powder, and black pepper until thoroughly mixed.
02 - Arrange an egg roll wrapper on a clean surface with one corner facing you. Spoon 2–3 tablespoons of filling onto the center of the wrapper.
03 - Fold the bottom corner over the filling, tuck in the sides, and roll upward tightly. Brush the top corner with beaten egg to seal. Continue with remaining wrappers and filling.
04 - Pour approximately 2 inches of vegetable oil into a deep-frying pot or heavy-bottomed saucepan. Heat oil to 350°F, monitoring with a thermometer.
05 - Working in batches, fry egg rolls in hot oil for 3 to 4 minutes, turning as needed, until golden brown and crisp. Remove with tongs and drain on paper towels.
06 - Arrange egg rolls on a platter and serve warm, accompanied by ranch or blue cheese dressing for dipping.