When making a classical version you carefully compose all the ingredients together; here we leave the eggs aside but gently mix everything else with the dressing.
In comparison to already published dressing by Ramsay, this one does not have capers, but includes shallots and replaces red with white vinegar. I think both are excellent and worth a head-to-head comparison. They keep well in the fridge for a couple of days.
For non-Americans the recipe at Serious eats will be harder to follow (cups and pounds). I did it more or less by following Kenji’s approach in the video. I also skipped additional anchovies and probably overcooked my potatoes; Gritzer cooks his potatoes 40 min, Kenji maybe 20?
Unlike Kenji I would definitely do the dressing in a separate bowl to better control the amount of dressing in the salad. Excellent and with some practice also rather quick!
J. Kenji López-Alt or youtube & Serious Eats, Daniel Gritzer