Begin by placing the petite white or red potatoes in a medium pot. Cover them with water and add a generous pinch of kosher salt. Bring the pot to a boil over high heat, then reduce to a simmer. Cook the potatoes for about 15 minutes until they are fork-tender yet firm to the touch, then drain them and set aside to cool slightly.

While the potatoes cool, grab a jar with a tight-fitting lid for the dressing. Combine extra-virgin olive oil, red wine vinegar, minced garlic, dry mustard, dried thyme, dried oregano, and a sprinkle of salt and pepper. Secure the lid and shake vigorously for about 30 seconds, until all the ingredients are well blended and emulsified.

Once the potatoes have cooled for about 10 minutes, chop them into bite-sized pieces and place them in a large mixing bowl.

Drizzle some reserved caper brine over the warm potatoes, then gently mix in Kalamata olives, sun-dried tomatoes, capers, red onion, and dill, stirring carefully to combine.

Pour the prepared dressing over the salad mixture and toss gently but thoroughly. Taste and adjust seasoning with additional salt and pepper if necessary.

Allow the salad to rest for at least one hour at room temperature for the best flavor. Just before serving, sprinkle crumbled feta cheese on top.