Begin by placing petite white or red potatoes in a large pot. Cover the potatoes with water, adding about an inch more, and stir in a generous pinch of kosher salt. Bring the pot to a rapid boil over high heat, then reduce the heat to medium-low. Let them simmer for approximately 15 minutes, or until a fork easily pierces the potatoes.

While the potatoes are boiling, combine extra-virgin olive oil, red wine vinegar, minced garlic, dry mustard, dried thyme, and oregano in a jar or a mixing bowl. Season with a pinch of salt and pepper. Seal the jar and shake vigorously, or whisk in the bowl until well blended.

Once the potatoes are cooked, drain them and let them cool for about 10 minutes. Cut the potatoes into bite-sized pieces.

In a large mixing bowl, gently toss the warm potato pieces with the reserved brine from the capers, chopped olives, sun-dried tomatoes, capers, diced red onion, and dill.

Pour the prepared dressing over the potato mixture and gently toss to coat everything. Adjust seasoning with more salt or pepper as needed.

Crumble feta cheese generously over the salad before serving. Let the salad rest in the refrigerator for at least one hour.