Rinse, peel and chop potatoes. Cook potatoes in salted boiling water, about 20 minutes. Drain. Press potatoes through a potato ricer or mash with a fork. Let cool.
Peel and chop onion. Rinse chives, shake dry and thinly slice crosswise. Mix mashed potatoes with oil, vinegar and broth. Stir in onion and chives and season with salt and pepper.
Rinse lettuce and dry in a salad spinner or between clean tea towels. Divide lettuce among four plates, top with bresaola and drizzle with potato vinaigrette.