In a blender or food processor, blend together the mayonnaise, sour cream, scallion, anchovy paste, parsley, 2 tablespoons chives, tarragon, and 2 teaspoons lemon juice, stopping and scraping down the sides occasionally, and blending until the dressing turns green.
Taste and blend in the remaining tablespoon chives and 1 teaspoon lemon juice, if desired.
Season the dressing with freshly ground black pepper.
DO AHEAD: The dressing can be prepared ahead and refrigerated, in an airtight container, up to 4 days.
