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 until just incorporated, taking care not to break up the crab meat.
02 - Position an egg roll wrapper on a clean surface with one corner facing you. Spoon 2–3 tablespoons of crab mixture into the center of the wrapper.
03 - Fold the bottom corner over the filling, then fold in the sides. Roll tightly away from you and seal the final edge with a small amount of water. Repeat with remaining wrappers and filling.
04 - Pour 2 inches of vegetable oil into a deep skillet or heavy-bottomed pot. Heat to 350°F.
05 - Fry egg rolls in batches, turning occasionally to ensure even cooking, until golden brown and crisp, approximately 3–4 minutes per batch. Transfer to paper towels to drain excess oil.
06 - Whisk together mayonnaise, Dijon mustard, lemon juice, hot sauce, salt, and pepper in a small bowl until smooth and fully combined.
07 - Arrange crab cake egg rolls on a serving platter and serve immediately with the prepared dipping sauce on the side.