Heat oven to 425° F. On a large rimmed baking sheet, toss the carrots, onions, 2 tablespoons of the oil, ¾ teaspoon salt, and ¼ teaspoon pepper.
Roast the vegetables, tossing once, until tender, 20 to 25 minutes.
Meanwhile, heat the remaining tablespoon of oil in a large skillet over medium-high heat.
Season the steaks with ½ teaspoon each salt and pepper. Cook to desired doneness, 4 to 5 minutes per side for medium-rare. Transfer to plates.
Add the wine to the skillet and whisk in the mustard. Simmer until slightly thickened, 1 to 2 minutes.
Stir in the tarragon. Serve the steaks with the sauce, carrots, and onions.