In a medium-size saucepan over high heat, boil potatoes until tender, 10–15 minutes, depending on size.
Rinse under cold water to stop cooking; then drain in a colander and let cool.
Meanwhile, in a medium-size bowl, whisk together yogurt, mustard, vinegar, and olive oil; add salt and pepper to taste.
When potatoes are cooled, mix with purslane in a bowl.
Add enough dressing to coat, and toss lightly. Serve at room temperature.