Scrub the potatoes well under running water, cut them in half, and place them in a medium-size saucepan. Cover them with cold water and bring to a boil over medium-high heat. Briskly boil the potatoes, uncovered, until they are just tender but still firm, 12 to 15 minutes. Take care not to overcook the potatoes.

Drain the potatoes in a colander and rinse them under cold running water to cool them down. Give the colander a few good shakes to rid the potatoes of excess water, and transfer them to a large bowl. Add the radishes, celery, cucumber, scallions, capers, dill, and chives to the potatoes.

Place the anchovy fillets, egg yolks, mustard, and garlic in a blender jar and puree, turning off the blender and scraping the inside of the jar as needed, until smooth.

Combine the two oils together in a small bowl. With the blender on low speed, drizzle the oils through the hole in the cover in a steady stream. Once the oils are added, you will have a thick emulsion, which is your own homemade mayonnaise.

Add the Worcestershire, lemon juice, cayenne, salt, and peppercorns and pulse the dressing to ensure a smooth mix.

Pour the dressing over the salad and give it all a good toss. Serve at room temperature, but because this is a mayonnaise-based salad, do not leave it at room temperature for long periods of time.