Place the petite white or red potatoes in a large pot, cover with cold water, add kosher salt, and boil. Reduce heat and simmer for about 15 minutes until fork-tender.

While potatoes are cooking, prepare the dressing by combining olive oil, vinegar, garlic, dry mustard, thyme, oregano, remaining salt, and black pepper in a jar or small bowl. Emulsify well.

Drain the potatoes and let them cool for about 15 minutes. Cut into halves or bite-sized pieces, drizzle with reserved caper brine.

In a large mixing bowl, combine cooled potato pieces, Kalamata olives, sun-dried tomatoes, red onion, and dill. Pour the dressing over and toss gently.

Taste the salad and adjust seasoning if needed. Before serving, sprinkle crumbled feta cheese on top.