Slice the onions thinly, cover them with vinegar, and set aside.

Scrub the potatoes, cover with cold water, and bring to a boil. Add kosher salt after the water has somewhat heated, the water should taste like sea water. Boil the potatoes until they are tender.

In the meantime, estimate about half the amount of dressing you'll need for your potatoes, and put that much simple vinaigrette into a large heatproof bowl. Transfer the hot potatoes into the bowl, and stir to coat with the dressing. Let cool.

Boil the peas or green beans in salted water until tender; for peas this will be very briefly. Transfer immediately into an ice bath to stop the cooking and keep them bright green.

Scoop the onions out of the vinegar and stir the onions, peas or green beans, and mayonnaise together with the dressed potatoes. Chill before serving.