01 - Gently combine 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 just until combined to maintain crab texture.
02 - Place an egg roll wrapper on a clean surface with one corner facing you. Spoon 2-3 tablespoons of crab mixture into the center. Fold bottom corner over filling, fold in sides, and roll tightly. Seal edge with water and repeat with remaining wrappers.
03 - Pour 2 inches of vegetable oil into a deep skillet or heavy-bottomed pot. Heat to 350°F, maintaining temperature throughout frying.
04 - Fry egg rolls in batches, turning occasionally, until golden brown and crispy, approximately 3-4 minutes per batch. Transfer to paper towels to drain excess oil.
05 - Whisk together mayonnaise, Dijon mustard, lemon juice, hot sauce, salt, and pepper in a small bowl until smooth and well combined.
06 - Arrange crab cake egg rolls on a serving platter and serve immediately with dipping sauce alongside.