Prepare the Potatoes - Peel the skin off the potatoes and cut them into ¾-inch cubes. Immediately place them in a large saucepan. Add enough cold water to cover them by 1 inch.
Cook the Potatoes - Bring the water to a boil over high heat. Once it starts to bubble, add 1 tablespoon salt and stir to dissolve. Reduce to a simmer over medium heat, adjusting as needed. Stir occasionally and cook until the potatoes are fork-tender but not falling apart, about 8 to 10 minutes.
Marinate with Vinegar - Drain the potatoes in a colander and transfer them back to the warm pot. Add the vinegar and use a rubber spatula to combine. Let it sit and marinate for 20 minutes. The potatoes will still be warm.
Combine the Ingredients - In a large bowl, gently stir together the potatoes, mayonnaise, celery, relish, onion, parsley, mustard, ¾ teaspoon salt, black pepper, onion powder, and chopped eggs. Season with salt and pepper to taste.
Chill then Serve - Cover and refrigerate until chilled, about 1 hour before serving. Garnish with more parsley, celery, and onion if desired.
Notes
Recipe Yield: About 5 cups
Serving Size: ½ cup
Storing: Store in an airtight container in the refrigerator for up to 2 days.
Freezing: Store in a resealable plastic bag for up to 1 month. Press into a flat layer, remove all of the air, and seal. Defrost in the refrigerator a day before serving.