01 - In a large bowl, 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. Mix until just combined, taking care not to overmix and break up the crab meat chunks.
02 - Place an egg roll wrapper on a clean, dry surface with one corner pointing toward you. Spoon approximately 2-3 tablespoons of the crab mixture into the center of the wrapper.
03 - Fold the bottom corner over the filling, then fold in both side corners. Roll the wrapper tightly away from you, sealing the final edge with a small amount of water. Repeat this process with the remaining wrappers and filling.
04 - Pour approximately 2 inches of vegetable oil into a deep skillet or heavy-bottomed pot. Heat the oil to 350°F, monitoring the temperature carefully with a thermometer.
05 - Fry the egg rolls in batches of 3-4, turning them occasionally with tongs, until golden brown and crispy, about 3-4 minutes per batch. Transfer the cooked egg rolls to paper towels to drain excess oil.
06 - Whisk together the mayonnaise, Dijon mustard, lemon juice, hot sauce, salt, and pepper in a small bowl until smooth and fully incorporated.
07 - Arrange the hot crab cake egg rolls on a serving platter alongside the prepared dipping sauce. Serve while hot and crispy for optimal texture and flavor.