Season the steaks with 1 ½ teaspoons salt and ¼ teaspoon pepper.
Heat 1 tablespoon of the oil in a large skillet over medium heat.
Add the steaks and cook to the desired doneness, about 4 minutes per side for medium-rare. Transfer to a plate; cover loosely with foil.
Meanwhile, wipe out the skillet. Heat the remaining 2 tablespoons oil over medium-low heat.
Add the carrots, parsnips, and beets. Cook until tender, about 7 minutes.
Season the vegetables with ½ teaspoon salt, ¼ teaspoon pepper, and the tarragon. Serve alongside the steaks.