Start by filling a large pot with cold water and adding a generous amount of kosher salt. Place the petite white or red potatoes into the pot, bring to a boil over high heat, and cook for about 15 minutes or until fork-tender. Drain and let cool slightly.

While the potatoes are cooling, combine extra-virgin olive oil, red wine vinegar, minced garlic, dry mustard, dried thyme, dried oregano, salt, and pepper in a jar or bowl. Shake or whisk until emulsified.

After 15 minutes, chop the cooled potatoes into bite-sized pieces and transfer to a large mixing bowl.

Add the reserved caper brine, pitted Kalamata olives, chopped sun-dried tomatoes, and thinly sliced red onion to the bowl. Toss gently to combine.

Pour the dressing over the potato mixture and stir carefully to coat without mashing the potatoes. Sprinkle fresh dill and crumbled feta cheese on top.

Let the salad sit for at least 1 hour at room temperature or refrigerate for a couple of hours for the flavors to meld.