01 - Combine shredded chicken, buffalo wing sauce, mozzarella cheese, blue cheese if desired, chopped celery, green onions, garlic powder, and black pepper in a large mixing bowl. Stir until evenly mixed.
02 - Lay an egg roll wrapper on a clean work surface with a corner facing you. Spoon 2 to 3 tablespoons of filling in the center. Fold the bottom corner over the filling, then fold in both sides, rolling tightly. Brush the top corner with beaten egg to seal.
03 - Continue filling and rolling remaining wrappers using the same method until all filling and wrappers are used.
04 - Pour vegetable oil into a deep, heavy-bottomed pot to a depth of about 2 inches. Heat oil to 350°F.
05 - Fry egg rolls in batches for 3 to 4 minutes per batch, turning as needed, until golden brown and crisp. Transfer to a plate lined with paper towels to drain excess oil.
06 - Serve egg rolls warm with ranch or blue cheese dressing for dipping.