1/4 cup buttermilk
4 tablespoons olive oil, divided
Kosher salt, freshly ground pepper
1 large Pink Lady apple, cored, thinly sliced
1 small parsnip, peeled, thinly sliced lengthwise on a mandoline
1 bunch arugula, tough stems trimmed
1/4 cup fresh dill with tender stems
2 tablespoons apple cider vinegar
Flaky sea salt (such as Maldon)
Whisk buttermilk and 2 tablespoons oil in a small bowl; season dressing with kosher salt and pepper.
Toss apple, parsnip, arugula, and dill in a large bowl. Drizzle salad with vinegar and toss to coat; season with kosher salt, pepper, and more vinegar, if desired.
Spoon half of dressing onto serving plates or a large platter. Add remaining 2 tablespoons oil to salad and toss to coat. Mound salad on top of dressing. Spoon remaining dressing over and season with sea salt.
Do ahead: Dressing can be made 2 days ahead. Cover and chill.