Season the steaks with 1 1/2 teaspoons of the salt and 1/4 teaspoon of the 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 and cover loosely with foil.
While the steaks rest, wipe out skillet. Heat the remaining oil over medium-low heat. Add the vegetables. Cook until tender, about 7 minutes. Season with the remaining salt and pepper and the tarragon. Serve alongside the steaks.
Tip: To save a few minutes of prep time, slice the vegetables into thin coins instead of cutting them into strips.