01 - Gently mix 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 until just combined. Avoid overmixing to prevent breaking up the crab meat.
02 - Place an egg roll wrapper on a clean surface with one corner pointing toward you. Spoon 2 to 3 tablespoons of crab mixture into the center. Fold the bottom corner over the filling, fold in both sides, then roll tightly. Seal the edge with a small amount of water. Repeat with remaining wrappers and filling.
03 - Pour 2 inches of vegetable oil into a deep skillet or heavy-bottomed pot. Heat the oil to 350°F, maintaining temperature throughout frying.
04 - Fry egg rolls in batches, turning occasionally, until golden brown and crispy, about 3 to 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 the dipping sauce on the side.