Preheat oven to 375 degrees.
Thinly slice potatoes and arrange on baking sheet. Drizzle with olive oil and place in oven. roast until golden brown and crispy, about 30 minutes. When they are done remove from oven and let cool.
Meanwhile in a small bowl whisk together, olive oil, garlic, balsamic, soy sauce and mustard. In a salad bowl toss together the purslane, potatoes, parsley and sliced radish with dressing.