Place halved potatoes in a large pot and cover with cold salted water by about 2 inches. Bring to a boil over medium-high heat, then reduce to a steady simmer. Cook for 12-15 minutes until fork-tender but still holding their shape.

While potatoes cook, bring another pot of salted water to a rolling boil. Add the trimmed green beans and cook for 4-5 minutes until bright green and crisp-tender. Immediately transfer to an ice bath to stop the cooking process.

In a small bowl, whisk together olive oil, white wine vinegar, and Dijon mustard until emulsified. Add minced garlic, fresh dill, and parsley, whisking until well combined. Season with salt and pepper to taste.

Drain both potatoes and green beans thoroughly. In a large serving bowl, combine the warm potatoes, cooled green beans, and sliced red onion. Pour the dressing over the vegetables while the potatoes are still slightly warm and gently toss everything together.

Taste and adjust seasoning with additional salt, pepper, or vinegar as needed. Let the salad rest for at least 30 minutes at room temperature, or refrigerate for 2 hours for best flavor development.