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.
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.