Preheat the oven to 425°F. Place the potatoes on a rimmed baking sheet and drizzle over the olive oil. Toss to coat then spread the potatoes out on the baking sheet and bake for 20 to 25 minutes, until golden brown and tender. Cool slightly.
While the potatoes are roasting, make the dipping sauce. Place the arugula, scallions, basil, and salt and pepper in a food processor or blender and pulse to chop, then run the machine to chop finely.
In a medium bowl combine the mayonnaise, sour cream, lemon juice and Worcestershire sauce, if using. Turn the herb mixture into the bowl and stir well to combine. Transfer to a small serving bowl and serve with the potatoes for dipping.