Set a steamer basket in a Dutch oven (or large pot with a lid), and add enough salted water to come just below basket; bring to a boil.
Place potatoes in basket, cover pot, and reduce heat to a gentle simmer. Steam potatoes, gently tossing occasionally, until tender, 15 to 25 minutes.
Meanwhile, in a large bowl, combine vinegar, scallion whites, 1 teaspoon coarse salt, and 1/4 teaspoon pepper.
Add hot potatoes to vinegar mixture; toss to combine. Cool to room temperature, tossing occasionally, about 1 hour.
Add mayonnaise and scallion greens to cooled potatoes; mix gently to combine. Serve, or cover and refrigerate up to 2 days.