Boil the petite white or red potatoes in a large pot of salted water for about 15 minutes until fork-tender. Drain and let cool.

In a mason jar, combine extra-virgin olive oil, red wine vinegar, minced garlic, dry mustard, dried thyme, dried oregano, salt, and pepper. Shake until emulsified.

Cut cooled potatoes into halves or bite-sized pieces. Transfer to a mixing bowl and drizzle with reserved caper brine, gently toss to coat.

Add kalamata olives, sun-dried tomatoes, rinsed capers, chopped red onion, and dill to the bowl. Toss gently.

Drizzle the vinaigrette over the salad and mix gently until well-coated. Adjust seasoning if necessary.

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