Place potatoes in a saucepan; cover with cold water to 2" above potatoes. Drain; let stand 10 minutes.
Add 1 Tablespoon vinegar. Bring to a boil; reduce heat, and simmer 10 minutes or until tender.
Combine basil, parsley, half of cheese, yogurt, mayonnaise, remaining 1 Tablespoon vinegar, 1 Tablespoon water, 1 ½ teaspoons lemon juice, and salt in the bowl of a food processor.
Pulse 8-10 times or until smooth.
Place potatoes in a medium bowl. Add pesto, toss to coat.
Combine remaining 1 teaspoon lemon juice and oil in a medium bowl, stirring with a whisk.
Add arugula, tomatoes, and remaining cheese, toss to coat. Place ½ cup salad on a plate, top with ½ cup of potatoes.