Heat oven to 400° F. Place potatoes on a plate and microwave, uncovered, on high for 12 minutes.
Meanwhile, heat the oil in an ovenproof skillet over medium-high heat. Season steak with ½ teaspoon salt and ¼ teaspoon pepper.
Cook steak for 1 minute per side. Transfer to oven and cook to desired doneness, 6 to 8 minutes for medium-rare. Transfer to a cutting board.
In a bowl, combine the sour cream, lemon juice, vinegar (if desired), 2 tablespoons water, 2 tablespoons chives, and ¼ teaspoon salt.
Divide the sliced steak, potatoes, and arugula among individual plates. Drizzle the potatoes and arugula with the sour cream mixture and sprinkle with the chives and ¼ teaspoon each salt and pepper.