Half-fill a large saucepan with water and 2 teaspoons salt. Bring to a boil. Add potatoes. Cook 10-12 minutes until tender but not falling apart. Drain, being careful not to break up potatoes. Meanwhile, heat grill. When it’s medium-hot, use tongs to place potatoes on grill and cook, turning to get grill marks on all sides, for 3-4 minutes. Place cooked potatoes in serving bowl and pour chimichurri or Romesco sauce over and toss gently. Taste for seasonings. Serve hot or at room temperature.