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 so the potatoes can be pierced with a fork or skewer (about 15 minutes). Use a spider or strainer to transfer the potatoes from the pot, reserving the hot water. Cut the potatoes in half and place in a bowl then while still warm, drizzle with 2-3 tablespoons of the vinaigrette dressing and set aside to cool.
Add the green beans to the pot of hot water and simmer for 1 minute or until the green beans turn bright green. Drain the water and set the beans aside to cool.
On a large platter, arrange the tuna, potatoes, green beans, halved tomatoes, boiled eggs, olives, red onion, capers, and hard-boiled eggs. Season with kosher salt and freshly ground black pepper and drizzle the salad with the vinaigrette or serve it on the side.