Originally in Gourmet Magazine; makes 1/2 cup

1 cup loosely packed fresh basil
1 1/2 tablespoons chopped shallot - or scallion
2 tablespoons balsamic vinegar
3/4 teaspoon salt
1/4 teaspoon black pepper
2 tablespoons mayonnaise
6 tablespoons extra-virgin olive oil

Put all ingredients in a blender and run until smooth.

Epicurious.com

1/2 cup plain low fat or non-fat yogurt
2 tablespoons white balsamic vinegar
1 tablespoon freshly squeezed lemon juice
2 tablespoons fresh basil leaves, roughly chopped plus 2 tablespoons sliced lengthwise into 1/4-inch strips
3/4 teaspoon shallots, chopped (about 1/4 small shallot)
1/4 teaspoon garlic, chopped (about 1/2 clove)
1/8 teaspoon sea salt
1/8 teaspoon freshly ground black pepper

Place everything but the julienned basil in a blender or food processor and blend until very smooth -- 1-2 minutes. Stir in basil strips at the end.