In a large Dutch oven, bring potatoes, 2 teaspoons salt, and water to cover by 2 inches to a boil over medium-high heat. Reduce heat; simmer until tender, about 10 minutes. Drain well. Place in a large bowl; sprinkle with vinegar and remaining ¾ teaspoon salt. Let cool completely.

Add green onion, celery, mustard, dill, oil, and pepper to potatoes, tossing to combine. Cover and refrigerate until chilled.