Place the potatoes in medium-sized pot and cover with water. Bring to a boil and cook until fork-tender, about 20-30 minutes. Meanwhile, in a large bowl, combine the yogurt and vinegar and whisk in the oil. Season heavily with salt and a pinch of cayenne.
Drain the potatoes, fill the same pot with water, and bring to a boil. Prepare an ice bath in a large bowl. Add the green beans and cook until crisp-tender, about 4 minutes. Shock in the ice bath and drain. Cut the potatoes into bite-sized pieces and combine with the greens beans, tomatoes, and dressing. Toss to combine and serve immediately or refrigerate.