Begin by washing the waxy potatoes thoroughly and placing them in a medium pot. Cover with cold water, ensuring there's about an inch of water above the potatoes. Add a pinch of kosher salt and bring to a boil. Cook for approximately 15 minutes, until fork-tender.

Drain the potatoes in a colander and let them cool slightly for about 5 minutes. Cut the potatoes into bite-sized chunks and set aside in a large mixing bowl.

In a clean jar, combine olive oil, red wine vinegar, minced garlic, dry mustard, oregano, thyme, kosher salt, and black pepper. Shake vigorously for about 30 seconds until well mixed.

Drizzle a tablespoon of caper brine over the warm potato chunks. Add the olives, diced red onion, capers, sun-dried tomatoes, and dill. Gently fold the ingredients together.

Pour the prepared dressing over the potato mixture. Gently toss until all ingredients are well-coated. Adjust seasoning if needed.

Crumble feta cheese over the salad and gently fold it in. Ensure every bite is infused with its creamy tang.

Cover the salad and refrigerate for at least an hour to meld the flavors. Serve warm or at room temperature, garnished with extra dill and feta.