Wash the small new potatoes thoroughly under cold running water until clean. Cut larger potatoes into halves or quarters so they are uniform in size, ensuring even cooking throughout.

Place the prepared potatoes into a large pot and cover them with cold water. Add a generous pinch of salt before bringing it to a boil over high heat; then reduce heat to simmer until tender when pierced with a fork, which should take about 15-20 minutes.

Once cooked through, drain the potatoes well in a colander and allow them to cool slightly at room temperature before proceeding with the next steps in your preparation.

While waiting for the potatoes to cool down, whisk together the extra virgin olive oil, fresh lemon juice, apple cider vinegar, Dijon mustard, and minced garlic in a small bowl until well combined; season it with salt and freshly ground black pepper according to your taste preference.

In a large mixing bowl, combine the cooled potatoes along with Kalamata olives, green olives, crumbled feta cheese, chopped parsley, and dill; ensure all ingredients are mixed together evenly for maximum flavor distribution.

Pour your prepared dressing over the potato mixture before gently tossing everything together until coated evenly; taste again for seasoning adjustments if necessary before serving immediately or chilling in the refrigerator for at least 30 minutes to let those wonderful flavors meld together beautifully!