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 incorporated to maintain crab meat texture.
02 - Position an egg roll wrapper with one corner facing you. Place 2–3 tbsp of crab mixture in the center. Fold bottom corner over filling, fold in sides, and roll tightly. Seal edge with water. Repeat with remaining wrappers and filling.
03 - Pour 2 inches of vegetable oil into a deep skillet or heavy-bottomed pot. Heat oil to 350°F.
04 - Fry egg rolls in batches, turning occasionally, until golden brown and crisp, 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 - Serve crab cake egg rolls immediately while hot with dipping sauce on the side.