Cover potatoes with 1 inch of water in stockpot or Dutch oven.
Bring to simmer over medium-high heat.
Reduce heat to medium and simmer, stirring once or twice to ensure even cooking, until potatoes are tender (a thin-bladed paring knife can be slipped into and out of center of potatoes with no resistance), 25 to 30 minutes for medium potatoes or 15 to 20 minutes for new potatoes.
Drain; cool potatoes slightly and peel if you like.
Cut potatoes into 3/4-inch cubes (use serrated knife if they have skins) while still warm, rinsing knife occasionally in warm water to remove starch.
Place warm potato cubes in large bowl.
Add vinegar, 1-2 teaspoon salt, and 1/4 teaspoon pepper and toss gently.
Cover bowl with plastic wrap and refrigerate until cool, about 20 minutes.
When potatoes are cool, toss with remaining ingredients and season with salt and pepper to taste.