Boil the potatoes until fork tender. Let them cool a little. Peel and cut them into 1-inch pieces.
Preheat the oven to 400°F.
Line a baking tray with parchment paper and spread the potatoes evenly on it. Drizzle with olive oil and sprinkle with salt. Mix well.
Roast for about 25 minutes, or until the potatoes are golden brown and crisp on the outside.
While the potatoes are roasting, add the cucumber, dill, chives, parsley, Greek yogurt, mayonnaise, both mustards, garlic, lemon juice, salt, and pepper to a large bowl. Mix until well combined.
Add the potatoes to the bowl. Gently toss everything together and serve.