Begin by washing the small new potatoes thoroughly under cold water. Cut larger potatoes into halves or quarters so that they cook evenly and uniformly.
Place the prepared potatoes into a large pot and cover them with cold water, adding a generous pinch of salt for flavor enhancement. Bring the water to a boil over high heat, then reduce it to a simmer, cooking until the potatoes are tender when pierced with a fork—this should take about 15-20 minutes.
Once cooked, drain the potatoes well in a colander and allow them to cool slightly before moving on to prepare your dressing.
While you wait for the potatoes to cool, whisk together olive oil, lemon juice, apple cider vinegar, Dijon mustard, and minced garlic in a small bowl until well combined. Season this mixture with salt and pepper according to your preference.
In a large mixing bowl, gently combine the cooled potatoes with Kalamata olives, green olives, crumbled feta cheese, fresh parsley, and fresh dill until everything is evenly mixed together.
Pour your prepared dressing over the potato mixture and toss gently until all ingredients are coated evenly in flavor-rich goodness. Taste your salad one last time; adjust seasoning if needed before serving immediately or chilling it for at least 30 minutes to allow all those wonderful flavors to meld beautifully together.