American-Style Potato Salad

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1/2 medium red onion, finely chopped

10 to 12 small waxy-style potatoes (about 2 pounds), peeled and quartered

2 tablespoons, plus 1 teaspoon kosher salt

2 stalks celery (with leaves), chopped

1 cup mayonnaise

1/4 cup chopped flat-leaf parsley

2 tablespoons pickle relish

1 tablespoon French's mustard

1/2 lemon, juiced

Freshly ground black pepper