We start with a pot of cold water, then add a tablespoon of vinegar to help the potatoes hold their shape. To make ahead, complete steps 1 and 2, and refrigerate. Toss together arugula mixture just before serving.
1 1/2 pounds fingerling potatoes, cut into 3/4-inch slices
Place potatoes in a saucepan; cover with cold water to 2 inches above potatoes. Add 1 tablespoon vinegar. Bring to a boil; reduce heat, and simmer 10 minutes or until tender. Drain; let stand 10 minutes.
Combine basil, parsley, 1 ounce cheese, yogurt, mayonnaise, sunflower seeds, remaining 1 tablespoon vinegar, 1 tablespoon water, 1 1/2 teaspoons juice, salt, and garlic in the bowl of a food processor. Pulse 8 to 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 5 ounce cheese; toss to coat. Place about 1/2 cup salad on each of 6 plates. Top each salad with 1/2 cup potato mixture. Sprinkle with dill.