Step 1

Whisk buttermilk and 2 Tbsp. oil in a small bowl; season dressing with kosher salt and pepper.

Step 2

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.

Step 3

Spoon half of dressing onto serving plates or a large platter. Add remaining 2 Tbsp. oil to salad and toss to coat. Mound salad on top of dressing. Spoon remaining dressing over and season with sea salt.

Step 4

DO AHEAD: Dressing can be made 2 days ahead. Cover and chill.