Place the potatoes in a large, wide pot, cover with cold water, and bring to a boil. Add 2 teaspoons salt, reduce heat, and simmer until the potatoes are just tender, 10 to 15 minutes. Drain and run under cold water to cool.
Meanwhile, in a large bowl, whisk together the oil, vinegar, mustard, and 1/4 teaspoon each salt and pepper.
Cut the potatoes in half (or quarter if large). Add the potatoes to the dressing and gently toss to coat. Fold in the lemon zest, chili flakes, scallions, parsley, and garlic.