Fill a large pot with cold water and add 1 tablespoon kosher salt. Add the whole potatoes and bring to a boil. When it comes to a boil, boil for about 5 to 8 minutes, depending on the size. Cook until fork tender (taste test to check).
Mince the shallot. Finely chop the dill and parsley. Thinly slice the green onions, if using.
When the potatoes are done, drain them. When they are cool enough to handle, slice them into bite sized pieces. Place the potatoes in a bowl and gently mix in the minced shallot, white wine vinegar, kosher salt, and 1/2 cup warm water. Let stand for 5 minutes, gently stirring occasionally. The potatoes will absorb the water as they stand.
Add the dill, parsley, green onions, drained capers, olive oil, and a few grinds black pepper. Taste and add additional salt if necessary (we added 1/4 teaspoon more). Serve warm or room temperature.