Place half of the mayonnaise or salad dressing, the parsley, chives, tarragon or white wine vinegar, anchovy paste or mashed anchovy fillets, garlic, and ground pepper in food processor bowl or blender container. Cover and process or blend until smooth. Transfer to a small bowl. Stir in sour cream and remaining mayonnaise or salad dressing. Cover and chill for 2 to 24 hours.
To serve, transfer the dip to a serving bowl. Cut jicama slices into desired shapes. Arrange jicama, sweet pepper strips, broccoli flowerets, and carrots around bowl. Makes about 1-1/2 cups dip (twelve 2-tablespoon servings).