Spray a grill basket with nonstick nonflammable cooking spray. Preheat the grill to medium-high heat.
Place the potatoes in the grill basket and grill until the potatoes are tender, turning once, about 10 minutes. Remove the potatoes from the grill and cool.
In a large bowl, combine the mayonnaise, parsley, basil, mustard, lemon juice, olive oil, salt and pepper.
Stir the creamy mixture into the potatoes, stirring until the potatoes are well coated. Serve at room temperature or chilled. Garnish with fresh basil or dill, if desired.
Cook's Note: During the show, Jamie used roasted potatoes instead of grilling them for the salad. Here's the recipe if you choose to do the same: In a large bowl, combine the potatoes, 3 tablespoons olive oil, 1 teaspoon salt, and 1/2 teaspoon pepper, tossing gently to coat. Arrange the potatoes, in a single layer, on a baking sheet. Bake at 350 degrees F until the potatoes are tender and lightly browned, stirring occasionally, about 35 minutes. Remove from the oven and cool.