First, make the vinaigrette by adding all of the ingredients to a jar fitted with a lid, close tightly, shake well, and set aside.
Add the potatoes to a medium pot and fill with enough water to cover the potatoes by 1 inch, then bring to a boil. Add 1-2 teaspoons of kosher salt, reduce to a rolling simmer, and cook until tender or when the potatoes can be pierced with a fork or skewer, about 15 minutes.
While the potatoes are cooking, bring a large pot of water to a boil, season with kosher salt, and add the green beans. Simmer for 1 minute or until the green beans turn bright green. Drain the water, rinse the green beans, and add to a large mixing bowl to cool.
When potatoes are finished cooking, use a spider or strainer to transfer them from the pot to a large bowl. As soon as the potatoes are cool enough to handle, cut them into bite-sized chunks (in half or quartered, depending on how big they are). Place the potatoes back in the bowl and while still warm, drizzle with 3-4 tablespoons of the vinaigrette dressing, then set aside to cool.
Add the green beans, then add the kalamata olives, red onion, and capers. Toss with the vinaigrette dressing, tarragon, and parsley. Taste for seasoning and add more salt and pepper to taste.
Stir in the diced hard-boiled egg or cut into quarters and nestle in the salad. To serve, top with more parsley if desired. This can be served warm, at room temperature, or chilled. Keeps in the refrigerator for 3-4 days.
