01 - Gently combine the crab meat, celery, red bell pepper, green onions, panko breadcrumbs, beaten egg, mayonnaise, Dijon mustard, parsley, Old Bay seasoning, cayenne pepper, salt, and black pepper in a large bowl. Mix until just combined, taking care not to overmix and break up the crab meat.
02 - Position an egg roll wrapper on a clean, dry surface with one corner facing toward you. Place approximately 2 to 3 tablespoons of the crab mixture in the center. Fold the bottom corner over the filling, fold in both sides, then roll tightly forward. Seal the final edge with a small amount of water. Repeat with remaining wrappers and filling.
03 - Pour about 2 inches of vegetable oil into a deep skillet or heavy-bottomed pot. Heat the oil to 350°F, maintaining consistent temperature throughout frying.
04 - Fry the egg rolls in small batches, turning occasionally to ensure even cooking, until golden brown and crisp, approximately 3 to 4 minutes per batch. Transfer to paper towels to drain excess oil.
05 - Whisk together the mayonnaise, Dijon mustard, lemon juice, hot sauce, salt, and pepper in a small bowl until smooth and well combined.
06 - Arrange the crab cake egg rolls on a serving platter and serve immediately while hot, accompanied by the prepared dipping sauce.