Place the potatoes and parsnips in a large pot. Cover with cold water and bring to a boil.
Add 2 teaspoons salt, reduce heat, and simmer until tender, 15 to 18 minutes.
Drain the potatoes and return to the pot. Mash with the milk, butter, scallions, ½ teaspoon salt, and ¼ teaspoon pepper.
Meanwhile, heat the oil in a large skillet over medium-high heat. Season the steak with ½ teaspoon each salt and pepper.
Cook the steak to desired doneness, 4 to 6 minutes per side for medium-rare. Let rest before slicing. Serve with the potato-parsnip mash.