Heat oven to 400° F.
Place the potatoes on a plate and microwave, uncovered, on high for 12 minutes.
Meanwhile, heat the oil in a large ovenproof skillet over medium-high heat. Season the steak with 1/2 teaspoon of the salt and 1/4 teaspoon of the pepper. Cook 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 using), 2 tablespoons water, the chives, and 1/4 teaspoon of the remaining 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 remaining salt, pepper, and chives.