Salt and ground black pepper
1 T white or apple cider vinegar
1 C finely diced new potatoes or red potatoes (about 3-4 potatoes)
1/4 C firmly packed fresh flat-leaf parsley leaves
3 anchovy fillets
6 green olives, pitted
1/4 C toasted walnuts
1 T lemon juice
3 T olive oil
1 celery stalk, halved vertically and thinly sliced
2 scallions, green and white parts, thinly sliced
Put the eggs in a saucepan with cold water to cover, 1 teaspoon salt and the vinegar. Bring to a boil, then decrease the heat and simmer, covered for one minute. Turn off the head and let the eggs sit in the water, covered, for 15 minutes. Drain the eggs and transfer to a bowl of ice water. When cool, peel and finely chop the eggs and put them in a large bowl.
Put the potatoes in a saucepan with cold water to cover and a dash of salt. Bring to a boil, then decrease the heat and simmer, covered, until just tender, about 4 minutes. Drain and let the potatoes cool. Add the potatoes to the eggs.
Combine the parsley, anchovies, olives, walnuts and lemon juice in a bowl of a food processor and pulse until coarsely ground. With the food processor running, slowly pour in the olive oil. The pesto should have a course texture, so turn off the machine once all of the oil has been poured in to prevent overprocessing.
Gently toss the pesto with the eggs and potatoes. Fold in the celery and scallions. Season with salt and plenty of pepper.