Place the quartered potatoes in a large pot and cover with cold, salted water. Bring to a boil and cook until fork-tender, about 15-20 minutes. Drain immediately.

While the potatoes are cooking, prepare the vinaigrette. In a small bowl, whisk together olive oil, lemon juice, dried dill, Dijon mustard, salt, and pepper until emulsified.

While the potatoes are still warm (this is key for absorption), transfer them to a large mixing bowl. Pour about half of the vinaigrette over the warm potatoes and gently toss to coat. Allow to cool slightly for about 10 minutes.

Add the diced red onion and chopped parsley to the potato mixture. Pour the remaining vinaigrette over the salad and toss gently again to combine all ingredients.

Gently fold in the crumbled feta cheese, being careful not to overmix, which can break down the feta too much.

Serve the salad immediately, or refrigerate for at least 30 minutes to allow flavors to meld. Taste and adjust seasoning (salt/pepper) before serving.