In a large bowl, combine the crab meat, mayonnaise, Dijon mustard, breadcrumbs, beaten egg, Old Bay seasoning, Worcestershire sauce, parsley, red bell pepper, green onion, salt, and pepper. Mix gently to avoid breaking up the crab meat too much.
Lay an egg roll wrapper on a clean surface with one corner pointing toward you (like a diamond). Place 2–3 tablespoons of the crab mixture near the center of the wrapper. Fold the bottom corner over the filling, then fold in the sides tightly. Brush the top corner with the beaten egg and roll tightly to seal. Repeat with the remaining wrappers and filling.
Heat about 2 inches of vegetable oil in a deep frying pan or pot over medium-high heat until it reaches 350°F (175°C). Fry the egg rolls in batches, turning occasionally, until they are golden brown and crispy, about 3–4 minutes. Remove with tongs and drain on paper towels.
In a small bowl, whisk together mayonnaise, lemon juice, Old Bay seasoning, and hot sauce to make the dipping sauce.
Serve the crab cake egg rolls hot with the dipping sauce on the side.