To begin, wash and cut the potatoes into 1 inch chunks. Do not peel the potatoes, only remove any rough patches.
Place the cut potatoes, water, vinegar, and 1 tsp sea salt in a Dutch oven or other large pot. Bring the potatoes to a boil, reduce heat to medium, and cook for 10-12 minutes, or until the potatoes are just fork tender.
While they are cooking, zest the lemon into a dish with the extra virgin olive oil. Juice the lemon into the dish. Add the remaining 1/2 tsp salt and the black pepper. Whisk these together with a vinaigrette whisk or other fine whisk until the dressing has emulsified. Set aside for now.
When the potatoes are done, drain them in a colander, then place them in a shallow dish with sides. Drizzle the dressing over the top of the hot potatoes and turn them gently to coat. Allow the potatoes to rest until they have come to room temperature.
Sprinkle in the minced parsley, chives, and shallot. Gently fold to combine.