From smittenkitchen.com
Preheat oven to 375°. Place walnuts on a rimmed baking sheet and toast in oven until fragrant, about 8 minutes. Let cool slightly, then coarsely chop and set aside.
Bring a medium saucepan of water to a boil. Add potatoes, and cook until tender, about 10 minutes. Using a slotted spoon, transfer potatoes to a colander to drain and cool. Set aside
Prepare an ice-water bath; set aside. Return pan of water to a boil. Add green beans, and cook until tender and bright green, about 3 to 4 minutes. Using a slotted spoon, transfer to ice-water bath to stop the cooking. Drain.
Whisk together vinegar, yogurt, mustard and 1/2 teaspoon salt in a small bowl; season with pepper. Add oil in a slow, steady stream, whisking until emulsified. Set dressing aside.
Arrange arugula, potatoes, and green beans on a platter. Season with remaining 1/2 teaspoon salt and 1/4 teaspoon pepper. Drizzle with dressing and sprinkle with toasted walnuts; toss to coat.