To Make Hard-Cooked Eggs: Place eggs in a single layer in a saucepan; cover with water. Bring to a simmer over medium-high heat. Reduce heat to low, cover and cook at the barest simmer for 10 minutes. Pour off hot water and run cold water over the eggs until completely cooled. To peel, crack the shell, then roll egg between your palms to loosen shell. Peel, starting at the large end. Rinse under cold water or dip in water to remove bits of shell.
Hard-cook eggs (see Tip). Peel eggs and chop coarsely.
Meanwhile, place potatoes in a large saucepan, cover with lightly salted water and bring to a simmer over medium-high heat. Reduce heat to medium and cook, covered, until just tender, 15 to 20 minutes. Drain; let cool for about 10 minutes.
Meanwhile, whisk mayonnaise, yogurt, oil, anchovy paste and pepper in a small bowl until smooth.
Cut potatoes into cubes and place in a large bowl. Add vinegar and salt; toss gently to coat. Add bell pepper, onion, celery, parsley, gherkins, capers, chives, chopped eggs and the mayonnaise mixture; toss to coat well. Cover and refrigerate until chilled, at least 30 minutes.