Place potatoes in a large pot, cover with cold water, add salt, and boil for about 15 minutes until fork-tender. Drain and let cool slightly.

In a mason jar, mix olive oil, red wine vinegar, garlic, dry mustard, thyme, oregano, salt, and pepper. Shake until emulsified.

Cut cooled potatoes into one-inch pieces and transfer to a large bowl while still warm.

Drizzle potatoes with caper brine, then mix in olives, onion, sun-dried tomatoes, and dill.

Pour dressing over the potato mixture and toss carefully to coat.

Gently fold in feta cheese before serving and let sit for at least one hour for flavors to meld.