Bring steak to room temperature. Season liberally with salt and pepper.
Cover potatoes with water, bring to a boil and cook to tender. Transfer to a bowl and lightly crack and crush them using a potato masher or the bottom of a water glass.
Stir together the buttermilk, crème fraiche or yogurt, EVOO, garlic, lemon zest and juice, mustard, salt and pepper. Toss the potatoes in the dressing to coat then fold in the onions and herbs. Adjust seasoning to taste.
Preheat cast-iron skillet or grill over medium-high heat. Drizzle the steaks with olive oil and cook 8-10 minutes, turning occasionally, until deeply browned and crusted; let rest.
For the Salsa Verde, place arugula in a food processor with salt, lemon zest and juice, capers, vinegar, chili flakes and walnuts or breadcrumbs. Pulse to finely chop then stream in EVOO until combined; transfer to serving dish.
Serve steaks topped arugula sauce with potato salad alongside.