Chicken is the usual protein. Chickpeas replace it here and do the job better than most substitutes — they hold their shape, they don't go stringy, and the salad was always really about the potato, pickle and egg.
Potatoes whole in salted water, 20–25 min, until a knife slides in with no resistance. Whole and skin-on is what keeps them from going waterlogged. Hard-boil the eggs in the same window: 10 min from boiling, then cold water.
Peel the potatoes while still warm — the skins slip off. Then let everything cool.
Do not dress anything warm. Warm potato plus mayonnaise turns to paste.
Dice the potatoes small. Chop 3 eggs, keep the fourth for slicing on top. Mash the chickpeas roughly with a fork, about half broken down — that is what gives the shredded-chicken texture. Fold together with the peas and pickles.
Whisk mayo, yogurt, lemon, salt, pepper and the brine if using. Fold through gently. Chill at least 2 hours, then taste again cold — it will want more salt and lemon than it did warm.