Whisk mayonnaise, Dijon, Worcestershire, lemon juice, Old Bay, smoked paprika, and egg in a large bowl until smooth.
Stir in green onions and parsley, then gently fold in crab meat to keep the lumps intact. Add panko just until the mixture holds together—sprinkle in more if it’s too wet.
Place an egg roll wrapper on a clean surface with a corner facing you. Add 2–3 tablespoons of crab filling, fold the bottom corner over, fold in the sides, and roll up tightly. Seal the edge with water and repeat with the rest.
Heat vegetable oil in a deep pot to 350°F (175°C). Fry 3–4 rolls at a time for 3–4 minutes, turning occasionally, until golden and crisp. Drain on paper towels.
Mix all remoulade ingredients in a small bowl, adjust seasoning, and chill until serving.